Answer:
By bike= 4 hours
By walk= 3 hours
Step-by-step explanation:
Given: Sydney travel by bike at 9 mph
Sydney travel by walk at 7 mph.
Total trip time= 7 hours
Distance to bookstore= 57 miles.
Lets assume the time spent travelling by bike be "x".
∴ Time spent travelling by walk is [tex](7-x)[/tex]
Now, lets find the distance travelled on bike and by walk.
we know, [tex]Distance= speed\times time[/tex]
∴ Distance by bike= [tex]9\times x= 9x[/tex]
Distance by walk= [tex]7\times (7-x)[/tex]
Using distributive property of multiplication.
∴ Distance by walk= [tex]49-7x[/tex]
Next, forming an equation for total distance travelled to find x.
⇒ [tex]9x+ (49-7x)= 57\ miles[/tex]
Opening parenthesis
⇒ [tex]9x+49-7x= 57[/tex]
⇒[tex]2x+49= 57[/tex]
Subtracting both side by 49
⇒[tex]2x= 8[/tex]
dividing both side by 2
⇒[tex]x= \frac{8}{2}[/tex]
∴[tex]x= 4\ hours[/tex]
Hence, time spent travelling on bike is 4 hours.
Subtituting the value x to find the time spent travelling by walk.
Times spent travelling by walk= [tex]7-4= 3\ hours[/tex]
hence, time spent travelling by walk= 3 hours
Molly makes cookies. She can make 2.5 batches in 1.75 hours. How many batches can she make per hour?
Answer:
Therefore she make 1.43 batches per hour.
Step-by-step explanation:
Given, Molly can make 2.5 batches in 1.75 hours.
Therefore she make [tex]=\frac{2.5}{1.75}[/tex] batches=1.43 batches per hour.
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
Answer:
The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of fliers the volunteers gave for a political campaign = 21/38
Remaining 612 were given out in another neighborhood
2. What is the total number of fliers they gave out?
x = Total of fliers
21x/38 = Fliers given out in the first neighborhood
612 = Fliers given out in the second neighborhood
Let's solve for x, this way:
x - 21x/38 = 612
38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)
17x = 23,256
x = 23,256/17
x = 1,368
The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.
Note: Same answer to question 14676213, answered by me yesterday.
Advertising a music festival, Paul saw a billboard while he was driving on the highway.
What is the best way, if any, to rewrite this sentence?
A.
While he was driving on the highway advertising a music festival, Paul saw a billboard.
B.
Advertising a music festival, Paul saw a billboard driving on the highway.
C.
no change
D.
While he was driving on the highway, Paul saw a billboard advertising a music festival.
The best way to rewrite the sentence is option D: "While he was driving on the highway, Paul saw a billboard advertising a music festival."
The original sentence is a bit awkward in its structure. Let's evaluate the options:
A. "While he was driving on the highway advertising a music festival, Paul saw a billboard."This option is incorrect because it suggests that Paul was the one advertising the music festival while driving, which is not the intended meaning.
B. "Advertising a music festival, Paul saw a billboard driving on the highway."This option is incorrect because it implies that the billboard itself was driving on the highway, which is illogical.
C. "No change"This option maintains the original structure of the sentence, which is awkward and does not convey the intended meaning clearly.
D. "While he was driving on the highway, Paul saw a billboard advertising a music festival."This option correctly places the modifier "advertising a music festival" next to "billboard," clarifying that it was the billboard, not Paul, advertising the music festival.
Which system of equations below has exactly one solution?
y=-8x - 6 and y = –8x + 6
y=-8x - 6 and 1/2y = -4x - 3
y=-8x - 6 and y = 8x - 6
y = -8x - 6 and -y = 8x + 6
Answer:
(y = -8x - 6 and y = 8x - 6) will have exactly one solution.
Step-by-step explanation:
1) Check number of solutions for A (using substitution)
y = -8x -6
y = -8x + 6
-8x - 6 = -8x + 6
+8x +8x
0 - 6 = 0 + 6
-6 = 6 (since this is false, it would be no solution)
2) Check number of sultions for B (using substition)
y = -8x - 6
1/2y = -4x -3
y = -8x - 6 (Multiply both sides of second equation by 2 to cancel out fraction on left side)
-8x - 6 = -8x - 6
Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution
3) Check number of solutions for C (using substition)
y = -8x - 6
y = 8x - 6
-8x - 6 = 8x - 6
+8x +6 = +8x +6
0 = 16x
x=0
The X value for the solution is 0, when we plug in this X value into one of the equations and solve for Y we will be able to get the Y coordinate
y = -8(0) - 6
y = -6
The solution for C will by (0,-6) which is one solution.
4) Check number of solutions for D (using substition)
y = -8x - 6
-y = 8x +6 --> y = -8x -6
muiltiply both sides of second equation by -1 to make the y positive
-8x - 6 = -8x - 6
Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution
2xp + 3y = 10
Solve for x
Answer:
x=5p-3/2py
Step-by-step explanation:
Im not entirely sure on this answer.
Your goal is to isolate x. So first subtract 3y on both sides resulting in 2xp=10-3y. Then u divide each side by 2p to get x by itself to get x=5p-3/2py.
the jellybean jar has a radius of 4.8 cm and a height of 11.8 cm. what would be a reasonable lower limit for the number of jelly beans in the jar
Answer:
[tex]\large\boxed{\large\boxed{100}}[/tex]
Explanation:
This question comes with four answer choices:
10,000100,0001001You just need to find a rough estimate of the volume of the jar and the volume of one jelly bean. This is called magnitude order.
The jellybean jar is cylindrical, Thus, its volume is [tex]\pi \times radius^2\times height[/tex]
To find the order of magnitude, you just use the numbers rounded to one signficant figure: round π to 3, the radius to 5, cm, and the height to 10:
[tex]Volume\approx 3cm\times (5cm)^2\times10cm=750cm^3\approx1,000cm^3[/tex]
The order of magnitude for the radius of a jellybean is 1 cm. And the order of magnitude of the volume of a sphere with a radius of 1 cm is the cube of the diameter (2cm):
[tex](2cm)^3=8cm^3\approx10cm^3[/tex]
Hence, a reasonable lower limit for the number of jellybeans in the jar is:
[tex]1,000cm^3/10cm^3=100[/tex]
To find a reasonable lower limit for the number of jelly beans in a jar with a radius of 4.8 cm and height of 11.8 cm, you can calculate the volume of the jar to be approximately 272 cm^3. Assuming the volume of a jelly bean to be approximately 1 cm^3, you can estimate the jar might hold at least 272 jelly beans.
Explanation:To calculate a reasonable lower limit for the number of jelly beans in the jar, a good starting point could be to calculate the volume of the jar and then consider the volume of a single jelly bean. Let's assume a jelly bean has an approximate volume of 1 cm^3 (though they can be bigger or smaller).
Given that the jar is cylindrical, we can calculate its volume using the formula for the volume of a cylinder: πr^2h, where r is the radius and h is the height. Here, radius = 4.8 cm and height = 11.8 cm.
Applying the values, we have: volume = π(4.8)^2 *11.8 = ~271.64 cm^3.
Dividing this volume by the volume of a single jelly bean gives us a rough estimate of the number of jelly beans that can fit in the jar. So, 271.64 cm^3 /1 cm^3 = 271.64, so roughly 272 jelly beans could be a reasonable lower limit, but you might be able to fit more depending on their actual size and how tightly they can pack together.
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Which values of p are solutions to the inequality shown? Check all that apply.
|18 – 2p| > 8
–10
–5
0
5
10
15
To find the values of p that satisfy |18 - 2p| > 8, we solve two separate inequalities, leading to the solutions p < 5 and p > 13. Hence, among the options provided, -10, -5, and 15 are the correct solutions.
Explanation:To solve the inequality |18 – 2p| > 8, we need to consider two cases because the absolute value measures distance from zero on a number line, either in the positive or negative direction.
Case 1: 18 - 2p > 8First, we solve the inequality when the expression inside the absolute value is positive:
18 - 2p > 8-2p > -10p < 5Case 2: 18 - 2p < -8Next, we solve the inequality when the expression inside the absolute value is negative:
18 - 2p < -8-2p < -26p > 13Combining the solutions from both cases, the values of p that satisfy the original inequality are p < 5 and p > 13. Among the given options, -10, -5, and 15 are the values that are solutions to the inequality.
Final answer:
The values of p that satisfy the inequality |18 - 2p| > 8 are p < 5 and p > 13; therefore, from the given options, -10 and -5 are the correct solutions.
Explanation:
The student needs to determine which values of p satisfy the inequality |18 – 2p| > 8. To solve this, we consider two separate cases because the absolute value function defines a piecewise function. The two cases are when the expression inside the absolute value is positive and when it is negative.
For the first case (18 - 2p > 0), we solve 18 - 2p > 8, which simplifies to -2p > -10, and upon dividing by -2 and flipping the inequality sign, we get p < 5. For the second case (18 - 2p < 0), we solve -(18 - 2p) > 8, which simplifies to -18 + 2p > 8, leading to 2p > 26, and upon dividing by 2, we get p > 13.
Therefore, the solution to the original inequality consists of all the values p < 5 and p > 13. Checking the provided options against these conditions, only -10 and -5 fall within p < 5, so they are the solutions to the inequality.
15 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the value of the expression shown below? 3 + (2 + 8)2 ÷ 4 × 1 over 2 to the power of 4
Answer:
The given expression is
[tex]3 + (\frac{(2+8)2}{4} \times(\frac{1}{2} )^4)= \hspace{0.3cm}3 +( \frac{10 \times 2}{4}\times \frac{1}{2^4} ) \hspace{0.3cm} = \hspace{0.2cm} 3 + ( \frac{5}{16})[/tex] = 3.3125
Step-by-step explanation:
The given expression is
[tex]3 + (\frac{(2+8)2}{4} \times(\frac{1}{2} )^4)= \hspace{0.3cm}3 +( \frac{10 \times 2}{4}\times \frac{1}{2^4} ) \hspace{0.3cm} = \hspace{0.2cm} 3 + ( \frac{5}{16})[/tex] = 3.3125
Answer:6 1/8
and i took the same test
Which mathematical statement is correct?
Answer:
B is the correct option.
Step-by-step explanation:
Place the values from the given options in equations of f(n) and g(n).
Write the answer of each of the following.
For instance, option A gives:
f(6)= 31
g(6) = 24
Option B gives:
f(7)= 63
g(10)= 36
Option C gives:
f(5)= 15
g(8)=30
Option D gives:
f(5)=15
g(5)=21
Thus option B is correct because f(7) is greater than g(10).
Answer:
B. f(7) > g(10)
Step-by-step explanation:
f(7) = 2⁶ - 1 = 63
g(10) = 3×10 + 6 =36
since 63>36 then f(7) > g(10)
:)
Where Is The Blue Dot On The Number Line?
Answer:
-2.1
Step-by-step explanation:
each line represents another 0.1, whether adding or subtracting.
after -22. there is one more tick mark, meaning it is -2.1
Answer:-2.1
Step-by-step explanation:
Each middle line is .1 and it is 1 under -2 so -2.1
How many cans will kyra be able to make from the sheet of metal
Kyra will make 9 cans from the sheet of metal.
Solution:
Height of the can (h) = 5 in
Radius of the can (r) = 6 in
The can is in the shape of a cylinder.
Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]
Surface area of the can = [tex]2 \times3.14 \times 6^{2}+2 \times 3.14 \times 6\times 5[/tex]
[tex]$=226.08+ 188.57[/tex]
[tex]=414.65[/tex]
Surface area of the can = 414. 65 in²
Area of sheet of metal = 3750 in²
To find how many cans able to make:
[tex]$\text { Number of cans} =\frac{\text { Area of sheet metal }}{\text { Surface area of the can }}[/tex]
[tex]$=\frac{3750}{414.65}[/tex]
= 9.04
Number of cans = 9
Hence Kyra will make 9 cans from the sheet of metal.
7h - 5(3h - 8) = -72
Answer:
h = 14
Step-by-step explanation:
7h - 5 (3h - 8) = -72
7h - 15h + 40 = -72
-8h + 40 = -72
-8h = -112
h = 14
Answer:
14
Step-by-step explanation:
7h-5(3h-8)=-72
7h-15h+40=-72
-8h+40=-72
-8h=-72-40
-8h=-112
8h=112
h=112/8
h=14
A recipe calls for 1/3 of a cup of milk for 10 cookies. How many cups of milk are needed to make 60 cookies?
Answer:
2 cups
Step-by-step explanation:
1/3 times 6 is 6/3, which is equal to two
Answer:
6/3 cups or simplified 2 cups
Step-by-step explanation:
The data set shown represents the total fee for miles
traveled on a toll road. Use the information to complete
the statements.
There are observed toll fee values.
It costs $ to travel 76 miles.
The predicted value for traveling 30 miles is $
Answer:
(Options 2,2,3)
There are 6 observed toll fee values.
It costs $3.40 to travel 76 miles.
The predicted value for traveling 30 miles is $1.61.
Answer:
There are 6 observed toll fee values.
It costs $3.40 to travel 76 miles.
The predicted value for traveling 30 miles is $1.61.
Step-by-step explanation:
If h(x) =(fog)(x) and h(x) = 3(x+2)^2, find one possibility for f(x) and g(x)
[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]
Explanation:In this case we have the composition of two function called [tex]f(x)[/tex] and [tex]g(x)[/tex] that results in another function [tex]h(x)[/tex]. So:
[tex]h(x) =(f\circ g)(x)[/tex]
Another way to write this function is:
[tex]h(x)=f(g(x)) \\ \\ So \ g(x) \ becomes \ the \ domain \ of \ f[/tex]
One possibility for [tex]f(x)[/tex] and [tex]g(x)[/tex] is:
[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]
Because [tex]h(x)=f(g(x))[/tex] is:
[tex]h(x)=3(x+2)^2[/tex]
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The Adams family has 10 children. The ratio of boys to girls in the Adams family is 1:1. How many girls are in the Adams family?
Answer:5
Step-by-step explanation:
In the Adams family with 10 children and a boy to girl ratio of 1:1, there are 5 girls.
Explanation:The question asked is about the number of girls in the Adams family which has a total of 10 children and the ratio of boys to girls is given as 1:1. When a ratio is 1:1, that means there is an equal number of each. So in the case of the Adams family, there are equal numbers of boys and girls.
To find the number of girls, we simply divide the total number of children by 2. Therefore, the number of girls in the Adams family is 10 ÷ 2 = 5. So, there are 5 girls in the Adams family.
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1/4 square yards of fabic divided into 8 equally sections. What is the size of each seaction in square yards?
Answer:
The size of each section is[tex]\frac{1}{32}[/tex] square yards
Step-by-step explanation:
Given:
Length of the fabric = 1/4 square yards
To Find:
The size of each section in square yards if divided into 8 equal sections
Solution:
Let the size of each section be x
Then
[tex]x = \frac{\text{length of the fabric}}{8}[/tex]
[tex]x = \frac{\frac{1}{4}}{8}[/tex]
[tex]x = \frac{1}{4} \times \frac {1}{8}[/tex]
[tex]x = \frac{1}{32}[/tex]
Then the length of each section will be [tex]\frac{1}{32}[/tex] square yards
Write a cosine function for the graph.
a.
y= 4 cos 2theta
c.
y= -4 cos 2theta
b.
y= 4 cos theta/2
d.
y= -4 cos theta/2
Answer:
Correct answer: y= 4 cos 2theta
Step-by-step explanation:
The Cosine Function
The general form of the cosine is
[tex]Y=A.cos(w\theta+B)[/tex]
where A is the amplitude, w is the angular frequency and B is the phase shift
The amplitude is the positive top value of the sinusoid or the most negative value. Since the sinusoid goes from -4 to 4, the amplitude is 4, thus
[tex]Y=4cos(w\theta+B)[/tex]
To find B and w, we use two points from the graph (0,4) and [tex](\pi/4,0)[/tex]:
[tex]4=4cos(w\times0+B)[/tex]
Simplifying
[tex]1=cosB[/tex]
Thus B=0
Now for the second point
[tex]0=4cos(w\times \pi/4)[/tex]
Or equivalently
[tex]\displaystyle \frac{\pi w}{4}=\frac{\pi}{2}[/tex]
Thus
w=2
Then, the cosine function is
[tex]Y=4cos2\theta[/tex]
Correct answer: y= 4 cos 2theta
The total amount of money (in cents) of x dimes and (x+6) nickels
Answer:
60 cents
Step-by-step explanation:
10x + 5(x+6)
15x = 30
x = 2
plug this back in the equation
20 + (5 x 8) = 60
The table below represents Bree's trip from her home to the library and back. On her way to the library, she travels at 6 miles per hour. On her way home, she travels at 12 miles per hour. The total travel time is 2 hours. Which equation can be used to find the distance in miles from Bree's house to the library?
The distance in miles from the house to the library is 8 miles.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Time to the library from home is d/6 hours
The time spend to reach home from the library is d/12 hours
Hence, the equation is;
d/6 +d/12 = 2 hours
Solving the equation:
2d+d= 24
3d=24
d=24/3 =8
Hence, the distance from the home to the library is 8 miles.
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write the inverse of the statement below. if you are over 18 then you can vote
Answer:
whats the statement
Step-by-step explanation:
Final answer:
The inverse statement is 'If you cannot vote, then you are not over 18,' but practical exceptions exist. The 26th Amendment ensures those over 18 have the right to vote, illustrating the importance of voting as a democratic right. Encouraging voter registration and participation among eligible citizens is crucial for maintaining a vibrant democracy.
Explanation:
The inverse of the statement 'If you are over 18 then you can vote' would logically be 'If you cannot vote, then you are not over 18'. However, this inversion doesn't always hold true in practice due to various voting laws and conditions, such as registration requirements and citizenship. The right to vote is a fundamental aspect of democracy, emphasized by constitutional amendments and various voting rights acts that seek to protect this privilege. For instance, the 26th Amendment to the U.S. Constitution, ratified on March 23, 1971, prohibits the denial of the right to vote for U.S. citizens eighteen years of age or older based on age.
To encourage political participation, it is vital for eligible citizens to register to vote and exercise their right. This act of voting allows individuals to have a say in how their government is run and who represents their interests. Discussions about lowering the voting age further, to include 16 and 17-year-olds, in local, state, or national elections have sparked debates about civic engagement and the readiness of younger citizens to participate in the electoral process.
5/6*2/3
9/10*5/18
4/5*3/4
2/3*5/1
To multiply fractions, you multiply numerator with numerator and denominator with denominator
In other words: a/b*c/d=(a*c)/(b*d)
So 1st one is (5*2)/(6*3) which is 10/18 or 5/9 simplified
2nd one is (9*5)/(10*18) which is 45/180 or 1/4 simplified
3rd one is (4*3)/(5*4) which is 12/20 or 3/5 simplified
4th one is (2*5)/(3*1) which is 10/3 or 3 1/3 if you want a mixed number
Hope this helped!
Answer:
Number one is 5/9
Number two is 1/4 that is the reduced fraction
Number three is 3/5 that is the reduced fraction
Number four is 3 and 1/3
Step-by-step explanation:
120% of x is equal to 78
Write an equation that shows the relationship of 120%, x, and 78
Answer:
[tex]\frac{120}{100}\times x=78[/tex] or [tex]12x=780[/tex]
Step-by-step explanation:
Given:
120% of x is equal to 78
We need to write an equation that shows the relationship of 120%, x, and 78
Solution:
We can write the 120% of x as:
⇒ 120% of x
Substitute [tex]\frac{120}{100}[/tex] in the place of 120%.
⇒ [tex]\frac{120}{100}\times x[/tex]
So, we write the equation as:
[tex]\frac{120}{100}\times x=78[/tex]
120 and 100 divided by 10.
[tex]\frac{12}{10}x=78[/tex]
Applying cross multiplication rule.
[tex]12x=780[/tex]
Therefore, equation shows the relationship of 120%, x, and 78.
[tex]\frac{120}{100}\times x=78[/tex] or [tex]12x=780[/tex]
Answer:
brainliest plsssssss
Step-by-step explanation:
answer is in the img below...
hope it helps you!!!!
if the quotient of 890 and 5 is decreased by 88 what is the difference
Answer:
90
Step-by-step explanation:
890÷5=178
178-88=90
Answer:
90
Step-by-step explanation:
890/5=78
178-88=90
90 = difference
Which could be the other dimension of the second photograph?
Answer:
15 inches
Step-by-step explanation:
Since the rectangles are similar then the ratios of corresponding sides are equal.
let x be the other dimension in the second photograph, then
[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{x}[/tex] ( cross- multiply )
4x = 60 ( divide both sides by 4 )
x = 15
Thus the other dimension in the second photograph is 15 inches.
the formula v=u+at is used to find speed of an object. find v if u=6,a=2 and t=5
Answer:
v = 16.
Step-by-step explanation:
This is one of the equations of motion when acceleration is constant.
v = 6 + 2*5
= 16.
Answer: v=16
Step-by-step explanation:
v=6+2(5)
v=6+10
v=16
A store makes a profit of $15 on a wallet, after a mark up of 60%, what is the selling priceof the wallet?
To find the selling price of the wallet after a 60% markup and a profit of $15, we need to calculate the original price of the wallet and add the profit to it. The original price of the wallet is $25 and the selling price is $40.
Explanation:To find the selling price of the wallet, we need to first find the original price of the wallet before the markup. Let's call the original price 'x'. Given that the store makes a profit of $15 on a wallet after a markup of 60%, we can write the equation:
x + 0.6x = x + $15
Simplifying the equation, we get:
1.6x = x + $15
0.6x = $15
x = $15 / 0.6
So, the original price of the wallet is $25.
The selling price of the wallet is the original price plus the profit, which is $25 + $15 = $40.
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What is the area of a regular hexagon with a side length of 5in and an apothem of 4.33in?
Answer:
64.95
Hope this helps :-)
Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify ( 6 x − 2 ) 2 ( 0 . 5 x ) 4 . Show your work.
Answer:
[tex]\frac{9x^6}{4}-\frac{3x^5}{2}+\frac{x^4}{4}[/tex]
Step-by-step explanation:
We want to simplify:
[tex](6x-2)^2(0.5x)^4[/tex]
We expand to get:
[tex](36x^2-24x+4)*\frac{x^4}{16}[/tex]
We expand further to get:
[tex]\frac{9x^6}{4}-\frac{3x^5}{2}+\frac{x^4}{4}[/tex]
Due: Wednesday, February 5, 2020 at 11:59 pm
Submit A
The students at Gregori were having a vote to decide on a new color. 5/8 of the students voted for blue. 5/9
of the remaining students voted for green. 48 students voted for red. How many students voted for blue and
green?
180 students voted for blue and 60 students voted for green
Solution:
Let "x" be the total number of votes
From given,
[tex]\frac{5}{8}[/tex] of the votes were for blue
[tex]Blue\ votes = \frac{5}{8}x[/tex]
Therefore,
[tex]Remaining = 1 - \frac{5}{8}x = \frac{8x-5x}{8} = \frac{3x}{8}[/tex]
Given that,
5/9 of the remaining students voted for green
So we get,
[tex]Green\ votes = \frac{3x}{8} \times \frac{5}{9} = \frac{5x}{24}[/tex]
[tex]Green\ votes = \frac{5x}{24}[/tex]
So we have now accounted for 5/8 (blue) + 5/24 (green) of the votes
Therefore,
[tex]Remaining = 1-(\frac{5x}{8} + \frac{5x}{24}) = 1 -(\frac{15x+5x}{24})= 1 -\frac{20x}{24} = \frac{24x-20x}{24}\\\\Remaining = \frac{4x}{24}\\\\Remaining = \frac{1x}{6}[/tex]
48 students voted for red
Therefore, remaining 1/6 votes for 48
Let "x" be the total number of votes
Then we can say,
1/6 of "x" is equal to 48
[tex]\frac{1}{6} \times x = 48\\\\x = 48 \times 6\\\\x = 288[/tex]
Number of votes for Blue:
[tex]Blue\ votes = \frac{5}{8} \times x = \frac{5}{8} \times 288\\\\Blue\ votes = 180[/tex]
Number of Green votes:
[tex]Green\ votes = \frac{5}{24} \times x = \frac{5}{24} \times 288\\\\Green\ votes = 60[/tex]
Thus 180 students voted for blue and 60 students voted for green