In a cafeteria, there are the same number of 3-legged stools as there are of 4-legged chairs. If stools have 120 fewer legs than chairs, how many people can sit in this cafeteria?

Answers

Answer 1
Imagine what x is quantity of stools. So
3x+120=4x
x=120
120 stools in cafeteria
120 chairs in cafeteria
120+120=240
There 240 people can sit in this cafeteria
Answer 2

The cafeteria can seat 120 people.

Let's denote the number of 3-legged stools as S and the number of 4-legged chairs as C. According to the problem, there are the same number of stools and chairs, so we have:

S = C

Next, we are told that the stools have 120 fewer legs than the chairs. Since each stool has 3 legs and each chair has 4 legs, we can set up the following equation:

3S + 120 = 4C

Since S = C, we can substitute C for S in the equation:

3C + 120 = 4C

Now, let's solve for C:

120 = 4C - 3C

120 = C

Now that we know there are 120 chairs, and since the number of stools is the same as the number of chairs, there are also 120 stools. Each chair can seat one person, and each stool can also seat one person, so the total number of people that can be seated is the sum of the number of chairs and stools:

Total seating = C + S

Total seating = 120 + 120

Total seating = 240

However, since there are only 120 chairs and 120 stools, and we cannot have half a piece of furniture, the maximum number of people that can be seated is the number of chairs or stools, which is:

Total seating = 120

Therefore, the cafeteria can seat 120 people.


Related Questions

Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive?
$3.50
$14.00
$84.00
$7.00

Answers

$14.00 is the answer because you have to multiply $69.98 by 20% and that will give you 13.99 but you round it off and you will get $14.00
The answer is C! Have a great day!!!

Six times a number decreased by ten is eight. Find the number.
A) 2
B) 3
C) 4
D) 5

Answers

The answer would be 3. 6*3=18-10=8 brainliest plz
The answer is B because 6x-10 = 8
6x = 18

Richard borrowed $950 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $85 from his paycheck each week. Assuming richard sticks to his promise, which of the following is not a possible scenario for the amount of debt Richard has remaining?

Answers

I think it's B but I'm not 100% sure


Answer:

B

Step-by-step explanation:

To solve this, you need to know first how many weeks will take Richard replacing the money.

We will call X the number of weeks so we say

$85 * X =$950

X= 11.17

This means it will take at least ≈12 weeks to pay his debt.

To know which scenario it's not possible, use the equation to choose the right option.

A: $85*5= $425

After 5 weeks, he paid $425, this mean he's $525 in debt.

B: $85*6= $510

After 6 weeks, he paid $510, this means he's $440 in debt.

C. $85*7= $595

After 7 week,s he paid $595, this means he's $355 in debt.

D. $85*8= $680

After 7 weeks, he paid $680, this means he's $270 in debt.

The not possible scenario is B because he will be paying at least $85 or more so he will debt $440 or less al week 6.

What type of transformation takes the graph of
f(x)=|x|
to the graph of
g(x)=â3+|x|
?
 


vertical translation of 3 units up

horizontal translation of 3 units right

vertical translation of 3 units down

horizontal translation of 3 units left

Answers

#1 vertical translation of 3 units up

Luigi is an urban planner. as an independent contractor, he charges $140 fee plus $ 25 per hour for each contract with the city.


Write a function to represent this scenario where Y represents the total amount her changes for a project and x represents the number of hours worked on a project

Answers

x = hours 25 per hour = 25x

y = total

 so y = 25x +140

Answer: y = 140+25x

Step-by-step explanation:

Since According to the question, Luigi initally charged $140.

And, per hour he charged an additional amount $25 for each contract with the city.

Here, x represents the number of hours worked on a project.

Thus the additional amount after x hours = 25x

So, the total amount he charged in x hours= 140+ 25x

And, according to the question y represents the above change.

Thus, we get a function for the given situtaion

which is , y= 140+ 25x , where x is number of hours and y is total amount charged.


What is the solution of the linear quadratic system or equations?
Y=x^2+5x-3
Y-x=2

Answers

The solution to the system of equations  are (1, 3) and (-5, -3)

Given the following functions

Y=x^2+5x-3

Y-x=2; y = x + 2

Equating both outputs will give

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Factorize the equation

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Recall that y = x + 2

y = 3 and -3

Hence the solution to the system of equations  are (1, 3) and (-5, -3)

Learn more here: https://brainly.com/question/20360246

Final answer:

The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).

Explanation:

To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]

Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]

Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]

Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).

Learn more about linear quadratic system of equations here:

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Solve the equation
5x - 5 = 3x - 9

A. 1

B. -2

C. -3

D. -1

Answers

The answer is B.) -2, hope it helps

An article with a net weight of 10 lb (pounds) is packaged in a box that weighs ½ lb. If 20 of these boxed articles are put into one freight container that weighs 15 lb, what is the gross weight?

Answers

10.5 per boxed article, multiply by 20 for 20 boxed articles then add 15 which is=
(10.5*20)+15= 225
or
In this question, a package of 10lb was put on a box with 0.5 lb weight. That mean every box would weight : 10lb + 0.5 lb= 10.5lb per box.

Then 20 of those boxes is put on a freight container with 15lb weight. Then the total weight should be:
20 boxes * 10.5 lb/box +15 lb= 210lb + 15 lb= 225lb

What are the steps for using a compass and straightedge to construct a square? Drag and drop the steps in order from start to finish. Use a straightedge to draw line a and label a point on the line as point P. Without changing the compass width, place the compass point on point S and draw an arc in the interior of ∠SPT . Use the straightedge to draw QS¯¯¯¯¯ and QT¯¯¯¯¯. Construct a line perpendicular to line a through point P. Label a point on this line as point R. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→ . Label the points of intersection as points S and T. Keeping the same compass width, place the compass on point T and draw an arc in the interior of ∠SPT to intersect the previously drawn arc. Label the point of intersection as point Q.

Answers

1. Use a straightedge to draw line a and label a point on the line as point P. 2. Construct a line perpendicular to line a through point P. 3. Label a point on this line as point R. 4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PRâ†â†’ . 5. Label the points of intersection as points S and T. 6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of â SPT to intersect the previously drawn arc. 7. Label the point of intersection as point Q. 8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of â SPT . 9. Use the straightedge to draw QSÂŻÂŻÂŻÂŻÂŻ and QTÂŻÂŻÂŻÂŻÂŻ.

Answer: The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

Here we have finished with the square RTQS.





What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? 5xy 15x3y 45x3y5 75x5y7

Answers

Answer: 15x3y

Step-by-step explanation:

We rewrite the expressions by using factorisation method of their primes. This will give:

60x4y7= 2×2×3×5×x×x3×y×y6

45x5y5= 3×3×5×x×x4×y×y4

75x3y= 3×5×5×x×x2×y

Common factors= 3 × 5 × x3 × y

= 15x3y

Answer:

its B

Step-by-step explanation:

In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. About how many times larger was the national debt in 2010 than 2003? THIS IS SCIENTIFIC NOTATION

Answers

Okay. 10^12 is 1 trillion. 1 trillion * 7 is 7 trillion. 14 trillion / 7 trillion is 2. The national debt in 2010 is two times larger than in 2003. So that basically means that the national debt doubled from 2003 to 2010.

Answer:  About 2 times.

Step-by-step explanation:

Given : In 2010, the national debt of the United States was about 14 trillion dollars.

We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]

then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]

dollars.

In 2003 it was about [tex]7\times10^{12}[/tex] dollars.

Now, the number of times the national debt was larger in 2010 than 2003 :-

[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]

Hence, national debt was about 2 times larger in 2010 than 2003 .

The probability of choosing either a girl or a boy is

Answers

It depends on the amount

No.of Girls / total no of boys and girls is boy's probabilty
And
No of boys / total no of boys and girls is girl's probabilty

Rose leaves her apartment to take her dog for a walk. She goes 3 blocks due south, 8 blocks due east, 5 blocks due north, and 8 blocks due west. At this point, where is Rose in relation to her apartment?

Answers

work shown above! in the end she is 2 blocks north of her apartment. hope this helps c:

Answer:

3 blocks due west

Step-by-step explanation:

Complete the expression so it forms a perfect-square trinomial. x² +___ x + 49 A. 14 B. 7 C. 7/2

Answers

(x + 7)(x + 7)

x^2 + 14x + 49

14x is your answer

hope this helps

The expression so it forms a perfect square trinomial is 14x.

We have given that,

The expression so it forms a perfect-square trinomial.

We have to determine the  x² +___ x + 49.

What is the factor?

A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.

In this case, one also says that n is a multiple of m.

(x + 7)(x + 7)

x^2 + 14x + 49

The expression so it forms a perfect square trinomial is 14x.

To learn more about the perfect square visit:

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You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?

Answers

4 sodas if you buy a bag of popcorn, if you dont buy popcorn you can buy 6 sodas

The law of detachment can be used to draw a conclusion from the following statements: "It will be sunny on Tuesday." "I will always go outside if the weather is nice."

Answers

Final answer:

Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.

Explanation:

The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:

If it is sunny on Tuesday (hypothesis).

I will always go outside if the weather is nice (conditional statement).

By applying the law of detachment, we can conclude that:

I will go outside on Tuesday (conclusion).

This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.

Amelia knits 1/10 of a scarf in 48 minutes. What fraction of a scarf can she knit in an hour? A. 5/24 B. 1/480 C. 1/8 D. 2/25

Answers

Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Twice a​ number, increased by one​, is between negative three and seven. find all the numbers.

Answers

Final answer:

To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.

Explanation:

The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.

To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.

First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.

-4 < 2x < 6

Now, divide all parts of the inequality by 2, which yields:

-2 < x < 3

All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.

Suppose that the length of a certain rectangle is 5 meters less than four times its width. the perimeter of the rectangle is 40 meters. find the length and width of the rectangle.

Answers

The length would be 15 meters and the width would be 5 meters

Amy, who is 17 years old, is 5 years older than twice Moe's age.Write an equation that you could solve to find Moe's age. Solve the equation and describe your steps.

Answers

(17-5) divided by 2 = 6 years old

First, take Amy’s age (17) and subtract it by 5, to get 12 ( 12 is 2 Times moe’s age). Then, divide 12 by 2 to get 6 ( since moe’s age was multiplied, you have to change it back by dividing).

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation. The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware. The total bill for the catering services is $1,512. Which equation can be used to determine the total number of guests, g, who attend the dinner party? 13.50g + 540 = 1,512 13.50g - 1,512 = 540 5400g + 13.50 = 1,512 540g - 1,512 = 13.50

Answers

13.50g+540=1512 

hope this helps :)

Answer:

The equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

Step-by-step explanation:

As given

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.

The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.

The total bill for the catering services is $1,512.

Total number of guests, g .

Than the equation becomes

1512 = 540 + 13.50 g

1512 - 540 = 13.50 g

972 = 13.50 g

[tex]g = \frac{972}{13.50}[/tex]

g = 72

Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

In a school election, 3/4 of the students vote. There are 1464 ballots. Write and solve and equation to find the number of students.

Answers

x = total number of students

equation is:

 (3/4)x = 1464

 to solve for x divide both sides by 3/4

x = 1464 / 3/4 = 1952

 x = 1952

 there are 1952 total students

parallelogram ESTA has vertices E (10,0), S(14,3),T(6,9) and A (2,6). to calculate its area, Jamal will first determine the equation of the line through point E and perpendicular to ST. What is the equation of this line?

Answers

closed line for the same equation. thanks for using brainly.

To determine the number of trout in a​ lake, a conservationist catches 180 ​trout, tags them and throws them back into the lake.​ later, 48 trout are​ caught; 12 of them are tagged. how many trout would the conservationist expect to be in the​ lake?

Answers

The ratio of the trout with tags that are caught and the total trout with tags is first calculated.

     r = 12 trout / 180 trout = 1/15

Then, we divide the number of trouts caught without tag by the value obtained above.

     N = (48 - 12) / (1/15) = 540

Then, we add the number obtained above and 180.
     T = 540 + 180 = 720

ANSWER: 720

anonymous 4 years ago A technical writer makes $45,000 per year and has just begun contributing 8% of her salary to her 401(k) plan. If her employer matches 6% of her contributions, how much will have been contributed to the 401(k) plan after 2 years?

Answers

add everything up except the 45,000 and 402(K). then subtract 45,000$ from 401. Then subtract your answers to both equations.

Answer:

$7,632 would have been contributed to the 401(k) plan after 2 years.

Step-by-step explanation:

A technical writer makes salary per year = $45,000

She contributing 8% of her salary to her 401(k) plan = 8% of 45,000

0.08 × 45,000 = $3,600

Her employer matches 6% of her contributions = 6% of 3,600

= 0.06 × 3,600 = $216.00

Total contribution for one year = 3,600 + 216.00 = $3,816

After 2 years = 3,816 × 2 = $7,632.00

$7,632 would have been contributed to the 401(k) plan after 2 years.

The height of a triangle is 4 cm more than twice the length of the base. the area of the triangle is 63 cm2. find the height of the triangle.

Answers

the answer is 14 inches.

Answer:

THE ANSWER COULD BE 14

given f(x)=x^3 and g(x)=1-5x^2, find (fog) (x) and its domain

Answers

(fog)(x) = f(g(x))

Given f(x) = x³ and g(x) = 1-5x²

Then
f(g(x)) = f(1 - 5x²) = (1 - 5x²)³

The domain of f(g(x)) is any real numbers; x ∈ R


Answer:

answer is b

Step-by-step explanation:


find the digit that makes 2,72_ divisible by 6

Answers

Well, the only options you have are between 1 and 9.

2,721/6= 453.5 Not 1

2,722/6=453.6 Not 2

2,723/6= 453.83 Not 3

2,724/6= 454 The last digit it 4

To find the missing digit to make 2,72_ divisible by 6, add the digit 4.

To find the digit that makes 2,72_ divisible by 6, we need to focus on the divisibility rules for 6. In this case, a number is divisible by 6 if it is divisible by both 2 and 3. For 2, the last digit must be even, and for 3, the sum of the digits must be a multiple of 3.

Given the number 2,72_, the blank digit needs to be 4 to make the number divisible by 6. This is because when the digit 4 is added, the number becomes 2,724, which is divisible by both 2 and 3.

if TRAP is an isosceles trapezoid what is the value of x ?

Answers

The answer I got is E. 19

the answer to this question is 19!

A mathematical scale in which the concentration of hydrogen ions in a solution is expressed as a number from 0 to 14

Answers

That is the pH scale
pH  = - log of the concentration of hydrogen ions in a solution.
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