A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. What is the cost of each table and each chair? And can you please explain the process using substitution please? Thanks.

Answers

Answer 1
4t+2c=200
2t+7c=400

I will solve for c in terms of t first
4t+2c=200
2c=200-4t
c=100-2t

Then I will substitute this in for c in the second equation to make it single variable
2t+7c=400
2t+7(100-2t)=400
2t+700-14t=400
300t=12
t=25 
Tables cost $25 each

Plug t back into one of the ORIGINAL equations to find the cost of chairs
4(25)+2c=200
100+2c=200
2c=100
c=50
Chairs cost $50 each

Hope this helps! :)



Related Questions

What is 3x+15-9=2(x+2) ?

Answers

SOLVING:

3X + 15 - 9 = 2(X + 2)
3X + 6 = 2X + 4
3X - 2X = 4 - 6
X = - 2  ===> The great answer.

TESTING:

[tex]3(-2)+15-9=2(-2+2)\\ \\-6+6=2(0)\\ \\\boxed{0}=\boxed{0}\quad\checkmark\ Correct.[/tex]
GOOD LUCK...!!

Density practice
A gas tank hold 50L. If the density of gasoline is 0.7 g/ml how much mass will the tank of gas have

Answers

the tank of gas will have a density of 35g

Using distributive property solve 4x39=n

Answers

The answer is 156. Hope that helped!!! ;)
The correct answer is 156

It takes 37 pounds of seed to completely play a 4 acre field how many acres can be planted per pound of seed

Answers

4 acres ÷ 37 pounds 
.108 acres per pound

Henry bought a movie tickets for himself and 6 of his friends.each movie ticket cost $7.85.How much money did Henry spend on tickets?

Answers

$54.95 would be the answer because Henry and six friends would be 7 time the cost of each movie ticket $7.85
Since 7.85*7=54.95 the answer is $54.95

Calvin Butterball is driving along the highway. He starts up a long, straight hill. 114 meters from the bottom of the hill Calvin's car runs out of gas. He doesn't put on the brakes, so the car keeps rolling for awhile, coasts to a stop, then start rolling backwards. He finds that his distances from the bottom of the hill 4 and 6 seconds after he runs out of gas are 198 and 234 meters, respectively. b.Write an equation expressing Calvin's distance from the bottom of the hill in terms of the number of seconds which have elapsed since he ran out of gas.

Answers

Final answer:

To determine Calvin's distance from the bottom of the hill in terms of the number of seconds since running out of gas, we can use the equation of motion for uniformly accelerated motion.

Explanation:

To write an equation expressing Calvin's distance from the bottom of the hill in terms of the number of seconds that have elapsed since he ran out of gas, we can use the equation of motion for uniformly accelerated motion.

Calvin's initial position at 0 seconds is 114 meters, and his final position at 4 seconds is 198 meters. Plugging these values into the equation:

d = vi x t + 0.5 x a x t²

we can solve for the acceleration, a:

a = (d - vi x t) / (0.5 x t²)

Substituting the values of d = 198m and t = 4s, we get:

a = (198m - 114m) / (0.5 x (4s)²)

After obtaining the acceleration, we can use the equation to find Calvin's distance from the bottom of the hill at any time after running out of gas.

The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.

Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000

(I have no idea how to do this. It's just extra credit but I need it)

Answers

The net amount they raise is the amount they receive minus what they pay in expenses.

They receive:
$10,000 fixed amount in donations
$55 per person

They pay:
$15 per person

If there are x number of entries, they receive 55x from the entries.
Also, they pay 15x for the entries.

The net amount they raise is amount they receive min us amount they pay:

55x + 10,000 - 15x

which simplifies to

40x + 10,0000

They want to raise at least $55,000.
At least $55,000 means $55,000 or more.
They want to raise an amount greater than or equal to $55,000.

Now we write the inequality:

40x + 10,000 >= 55,000

Now we solve the inequality for x, the number of entries.

40x >= 45,000

x >= 1125

They must have 1125 or more race entries to raise $55,000.

You put $800 in a savings account at 4% annual interest and leave it there for five years. What is the principle?_____

Answers

at the end of five years, you will have made 160 dollars on interest,  a total of $960, because four percent of 800 is 32, and you multiply that by 5 years to get 160.

Circle the ordered pairs that are solutions to the inequality y - 2x < - 1.

(1, 0)
(0, 1)
(0, -1)
(-1, 0)
(3, 2)
(-2, -4)
(2, 4)
(-4, 2)
(0, 0)

Please help!

Answers

All we have to do, is plug in the ordered pairs, and see which ones are true to the equation. (x,y)

(1,0) After plugging those into the equation we get: 2<-1. this is not true, so this answer is false.

I continued this all the way down the line:

(0,1)= 1<-1 = false
(0,-1)=-1<-1=false
(-1,0)= -2<-1=true
(3,2)=-1<-1=false
(-2,-4)=2<-1=false
(2,4)=2<-1=false
(-4,2)=8<-1=false
(0,0)=0<-1=false

There is only one true ordered pair for this equation:

(-1,0)


The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the garden.

Answers

Set the following: Length = L    Width = W

The length is twice the width:    L = 2*W     or:  W = L/2

Perimeter: P = 60ft = 2*L + 2*W

Substituting L for W in the perimeter equation gives:

P = 60ft = 2*L + 2*(L/2) = 2*L + L = 3L

L = 60ft/3 = 20ft    W=L/2=20ft/2=10ft

Verify result:  Perimeter= P = 60ft = 2L + 2W = 2*20ft +2*10ft = 40ft+20ft = 60ft

The area of the rectangular is: Area = A = Length*Width = L*W = 20ft*10ft = 200 (ft)^2

Hopefully This Helps!!

Final answer:

To find the area of a rectangle when the perimeter is given, determine the dimensions using the relationship between length and width and then calculate the area. In this case, the area of the garden is 200 square units.

Explanation:

The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the garden.

Let the width of the rectangle be x. Therefore, the length is 2x.

The perimeter of a rectangle is given by 2(length + width), which in this case is 2(2x + x) = 60 units.

Solving for x, we get x = 10. Therefore, the width is 10 units and the length is 20 units. The area of the garden is length x width = 20 x 10 = 200 square units.

how do you simplify -7 |7|

Answers

Negative 7 times the absolute value of 7
negative times a positive is a negative
so -7*7= -49
The answer is:  " - 49 " .
_____________________________
The problem:  "What is "-7" multiplied by "the absolute value of (7)"?

Note:  The absolute values of (7) = 7 ; that is the absolute values of (positive 7) is:  "(positive 7)" .
__________________________
  So, we are left with:  What is: "-7 " multiplied by  "+ 7" ; 
           {i.e. ,  " (-7)*(7) = ? " } ;
_________________________
The answer is:  " -49 " .
_________________________

How to simplify each expression
2/3(7w + 4) - 1/3 (2w - 1 )

(3-7m) +2(3.5m+ 1)

Answers

  14 w /3  + 8/3  - ( 2/3w  -1/3 )   =  
14w/3  + 8/3 -2/3 w +1 /3 = 

12w /3  + 9/ 3 = 3  ( 4w +3) / 3  =  4w +3  

the second 
 3-7m +7m+ 2 = 5 





A truck driver drove 120 miles in 1 3/4 hours what is the speed of the truck in miles per hour

Answers

20 would be the correct
answer

its 120mi÷1.75hours=68.6miles per hour

Lisa has a certain amount of money. She spent 39 dollars and has 3/4 of the original amount left. How do you write this equation?

Answers

Let’s call the amount of money she started with “m”.

What this problem is saying is that “taking away 39 from m is equivalent to taking 3/4 of m.” What do “taking away 39 from,” “equivalent to,” and “3/4 of” translate to mathematically?

A ball always bounces to 3/5 of the height from which it falls. It falls from a height of 1meter how high will it rise after the second bounce?

Answers

this is the answer check it out
Final answer:

After the second bounce, the ball will rise to a height of 0.36 meter.

Explanation:

To find the height the ball will rise after the second bounce, we can use the given information that the ball always bounces to 3/5 of the height from which it falls. In this case, the ball falls from a height of 1 meter.

For the first bounce, the ball rises to 3/5 of 1 meter, which is 0.6 meter. For the second bounce, the ball will rise to 3/5 of 0.6 meter. To calculate this, we multiply 3/5 by 0.6 meter, which gives us 0.36 meter.

Therefore, after the second bounce, the ball will rise to a height of 0.36 meter.

Which symbol correctly compares the two fractions? Use > , < , or =. Enter your answer in the box. 2/4 3/8

Answers

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8. They are 2/4 and 3/8, respectively.

what are symbols ?

something that represents another item. especially: something tangible that denotes or implies something else that is not itself imaginable or demonstrable. The lion is a representation of bravery. an alternative to a word or combination of words, such as a letter, character, or sign.

given

= 2/4 = 0.5

= 3/8 = roughly 0.37

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8.

To know more about symbols visit :-

https://brainly.com/question/17310967

#SPJ1

Final answer:

To compare 2/4 and 3/8, simplify 2/4 to 1/2, then convert to eighths, resulting in 4/8. Since 4/8 is greater than 3/8, 2/4 is greater than 3/8.

Explanation:

To compare the fractions 2/4 and 3/8, we need to find a common denominator or convert them to a common form such as decimals.

The simplest way is to notice that 2/4 can be simplified to 1/2.

Now, if we convert 1/2 to eighths, we get 4/8 because we multiply both the numerator and denominator by 4 to get the common denominator of 8 (1 x 4)/(2 x 4) = 4/8.

Comparing 4/8 with 3/8, we can see that 4/8 is larger than 3/8, as 4 is greater than 3.

Hence, the correct inequality symbol to compare 2/4 and 3/8 is ">".

According to the transitive property of inequality which states that if a > b and b > c then a > c, if 4/8 > 3/8 and 2/4 is equal to 4/8, then 2/4 > 3/8.

what is 0.13 +(-5.7)

Answers

The correct answer would be -5.57

find a pair of 3 digit numbers that have an estimated difference of 520

Answers

the answer is 250 and 770

Pat has nine cards. Frank has two more cards than Steve. Steve has 3 cards how many more cards does Pat have than Frank?

Answers

pat =9
steve = 3
frank = 5 (3+2)
9-5 = 4
answer is 4

Based on the information given, Pat has 4 more cards than Frank.

The number of cards that Pat has = 9 cards

Number of cards that Steve has = 3 cards

Since Frank has two more cards than Steve, the total number of cards that Frank has will be: = 3 + 2 = 5

In order to know the number of cards that Pat has more than Frank, we will have to calculate the difference between the cards that they've. This will be:

= Pat's card - Frank's card

= 9 - 5

= 4

Therefore, Pat has 4 more cards than Frank.

Read related link on:

https://brainly.com/question/1902152

find the sum of the first 13 terms in the series -5+1+7...+67

Answers

this is an arithmetic series with common difference 6 

S13  = (13/2)[2*-5 + (13-1)*6)]  =  403

Write using algebra.
If Jim is x years old now, and his sister is twice as old, how old was his sister 7 years ago?

Answers

I think his sister would be 7, 7 years ago but I'm not sure
The answer is 2x-7

And this needs to be 20 characters (so don't mind this)

3(x+1)-2(3x+7) i need help with this question

Answers

First distribute

3x + 3 - 6x - 14

Simplify 

-3x - 11

solve for x

-3x  = 11

-3x/-3 = 11/-3

x = -11/3

hope this helps
3(x + 1) - 2(3x + 7)

3x + 3 - 6x - 14

(3x - 6x) + (3 - 14)

-3x - 11

hope this helped, God bless!

Find (18 × 106) + (5 × 104). A) 1.8005 × 106 B) 1.8005 × 107 C) 1.805 × 106 D) 1.805 × 107

Answers

D.) 1.805 multiplied by 107

5 less than the quotient of a number and 3 is -7

Answers

[tex] \frac{x}{3} [/tex]  -  5  =  -7  .
____________________________________________
This would be one way to write the expresion/equation; in which "x" represents the unknown number.

Now, to solve for "x" ;
____________________________________________
Given:
____________________________________________
[tex] \frac{x}{3} [/tex]  -  5  =  -7  ;

Add "5" to EACH SIDE of the equation:
_____________________________________________
[tex] \frac{x}{3} [/tex]  -  5  + 5 =  -7  + 5 ;

to get:

[tex] \frac{x}{3} [/tex]  = -2 ;

x = (-2 * 3) ;
_________________________________
x =  - 6 .
_________________________________

Alan travels 3/10 of his journey car. 3/20 by bicycle 1/12 by boat and walks the rest what fraction of the journey did he walk? If the journey is 140 km,how many km did he walk?

Answers

The denominators are: 10, 20, and 12
The LCD (lowest common denominator) is 60 as this is the smallest multiple of 10, 20, and 12.

Get each fraction to have a denominator of 60
3/10 = (3/10)*(6/6) = (3*6)/(10*6) = 18/60
3/20 = (3/20)*(3/3) = (3*3)/(20*3) = 9/60
1/12 = (1/12)*(5/5) = (1*5)/(12*5) = 5/60

The fractions 
3/10, 3/20, and 1/12
are equivalent to
18/60, 9/60, and 5/60
in that exact order

Add up the second set of fractions to get
(18/60) + (9/60) + (5/60) = (18+9+5)/60 = 32/60 = 8/15

The result of adding the fractions and reducing leads to 8/15 meaning that Alan takes 8/15 of the journey to use his car, bike and boat

The rest of the journey (7/15) is done walking
Multiply this with the total distance 140
(7/15)*140 = (7/15)*(140/1)
(7/15)*140 = (7*140)/(15*1)
(7/15)*140 = (980)/(15)
(7/15)*140 = (975+5)/15
(7/15)*140 = (975/15)+(5/15)
(7/15)*140 = (65)+(1/3)
(7/15)*140 = 65 & 1/3

The answer as a mixed number is 65 & 1/3
The answer as an improper fraction is 980/15
The approximate answer in decimal form is 65.33 (rounded to 2 decimal places)

David charges $15 plus $5.50 per hour to mow lawns Arie charges $12 plus $6.25 per hour to mow lawns. In what situation is Aries charge greater than or equal to David’s charge?

Answers

Aries's charge will be greater than it equal to David's charge if they are charging to mow for 4 or more hours.

Solve for x. -16 = 8x/5
x = 10
x = -10
x = -25

Answers

- 16 = 8x/5

solve equations



step 1 simplify both sides of the equation.

- 16  = 8/5x



step 3 flip the equation

8/5x = - 16


step 3 multiply both sides by 5/8

( 5/8) * ( 8/5x) = (5/8) * ( - 16)

x = - 10


answer x = - 10

The table below show 2 equations. Equation 1: 3x-1=7+2 Equation 2: 2x+1+4=3 which statement is true about the solution to the two equation?

Answers

You have not added your options, so I will just solve and hope that my answer is in your choices.

For the first equation we have:
3x-1=7+2
3x = 7+2+2
3x = 10
x = 10/2

For the second equation we have:
2x+1+4=3
2x = 3-4-1
2x = -2
x = -1

Therefore, there isn't a solution that satisfies both equations. Based on this, this system of equations has no solution.

The answer is d

i hope this helps

Tony spent $11.52 for some pens that were on sale for $.72 each how many pens did Tony bye

Answers

he will bye 16 pens hope that helps u

PLease help ME!!!!!!!!!!!!!!!!!!


Conduct a poll of adults and students in your area. Ask them how much time they spend online each week that is not for work or school. Describe how you conducted the poll and record the results of the poll in an organized manner below.

Answers

Most of the adults in my community spend 43% of their time online that is not used for work or school.

And most of the children in my Community spend 53% of their time online without working.
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Algebraically determine if the relation y = x3 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry. Last word) the inverse dependency ratio is predicted to fall to about 1.16 by 2050. what is the most likely effect of this decline? multiple choice it will likely cause worker productivity to decline. the social security system will be on stronger financial footing. innovation will increase significantly as dependents take advantage of their otherwise idle time. living standards will fall if productivity gains don't sufficiently offset the decline in the ratio. which of the following equations represents a proportional relationship? Choose all that apply.A. x=2yB.a = 1/3bC.4x=y-2D.7/3x=nE.1/2=1/4 During which circumstance is the inherent powers of the president most likely to expand Shaniqua starts a bank account with a $120 deposit. By the end of 12 months, she hopes to have saved $900. She knows that she can save $30 per month from her paycheck, but can earn some extra money by tutoring on the weekend. How much extra per month does Shaniqua need to save in order to meet her goal? Select the equation that best represents this situation and solution. Write the ratio using fraction notation and reduce. 20 minutes to 1 hour(a) 20(b )1/3(c) 1/20(d) 3 The center of the Chaldean empire was at 1. Nineveh 2. Jericho 3. Catal Hyk 4. Babylon When Samuel was a kid, his family had a dog. It wasn't a purebred or anything, just a mutt, but Samuel's family loved it very much. They only owned the one dog, but they loved all dogs, every dog they saw. When they would take the mutt to the dog park, Samuel and all of the members of the family would pet every dog they saw and scratch them behind the ears and say things like, "Aren't you beautiful!" But there was something else they all agreed on, too: cats were terrible! For reasons no one knew, Samuel's family was one of those families that loved dogs but hated cats. And so, Samuel grew up hating cats too. When Samuel was 18, he left home for college, and still he hated cats. Samuel and his friend Max rented an apartment in college. One night, they were watching TV when Max said, "There is something wrong with this apartment. It just doesn't feel right without an animal. I think we should get a cat." Samuel agreed that it didn't feel right without an animal, and he knew that dogs weren't allowed in the apartment. But, he hated cats, so he said, "You can get one if you want, but I'm not paying for anything!" So Max bought a cat and named it Mitsy, and Samuel refused to help take care of it. Still, he was around the cat a lot. After a few weeks, he began to like it when the cat would rub her head on Samuel's leg, and he liked how she stalked and pounced on roaches. Within two months, Samuel thought Mitsy was one of the greatest animals in history. He was sure his family would make fun of him when they found out! 19 What is a recurring theme in a story such as this? A. Once a person has an opinion, he or she should never change it. B. It is important to hold the same opinions as one's family. C. No one can like both dogs and cats equally. D. A person should form his or her own opinions. What will happen to the ecosystem if the paddlefish are hunted in excess Identify the characteristics of the two subclasses of bony fishes Three metal spoons are on table. They are at room temperature. If the three spoons touch. A. Heat will flow among the three spoonsB. Heat will flow between two spoonsC. No heat will flow among the spoonsD. Heat will flow from the spoons to the air The many natural waterways provided cheap movement of goods to market. a. True b. False Formula for Area of this one. Which one is the base x height. Show your work. 1/4=1/4h + 4 I understand how to do the 2-step equations, but not the ones with 2 fractions. The cpi for "all items" was 233.707 in january 2015, and 236.916 in january 2015. over this period, the rate of inflation as measured by the rate of change of the cpi was How does victor view his switch to mathematics what does he compare it to? Things fall apart how did ear respond when mosquito asked if she would marry him How did loess influence the development of early Chinese civilizations? To avoid flooding caused by settled loses raising the Huangs water level, peasants had to maintain dies.To limit erosion caused by loses, people had to plan to regularly clear public paths and roads.To protect crops against destructive loses storms, farmers had to set up networks of windbreaks.To prevent invaders from using loses bridges to cross the Huang, soldiers had to be posted to keep watch. what is the 3sqaure root of 0.027y^9 = ? Identify which atomic orbitals are used to construct the specified sigma bonds: g Steam Workshop Downloader