Question

It costs a family $324.00 to buy a ten-ft-by-12-ft rug. If the cost is proportional to the area, what will it cost the family to buy a 15-ft-by-18-ft rug?

Answer 1

Do you know what it means for the cost to be proportional to the area?

Answer 2

no

Answer 3

This means there is some constant, let's call it, k such that
cost=k*area

Answer 4

ok now we have an equation
do you know how to find the area of a 10 ft by 12 ft rug?

Answer 5

multiply them?

Answer 6

right

Answer 7

so the area=10*12 ft^2 when we have the cost is 324



this is a point on our line cost=k*area

use this point (area=10*12, cost=324) to find k

Answer 8

solve for k
and I will check your k

then we will move on to the final question of this problem

Answer 9

I am very confused

Answer 10

we were given cost=k*area when it told us that the cost was proportional to the area

we were also given when the area=10*12 we have the cost=324

this is enough information to find our constant of proportionally (aka k)

Answer 11

you need to enter area=10*12 and cost=324 into cost=k*area
to find k

do you still not understand what I'm asking you to do? please let me know.

Answer 12

324=k*120

Answer 13

right solve for k

Answer 14

324/120=2.7

Answer 15

cool so you just found the constant of proportionality

Answer 16

so we can find the cost for any area rug

or

find the area of the rug given the cost

Answer 17

so we have
cost=2.7*area

Answer 18

what will it cost the family to buy a 15-ft-by-18-ft rug

this is your question

Answer 19

you are given the area basically and you are asked to find the cost
using the equation cost=2.7*area

Answer 20

cost=2.7*270
cCost=$729.00

Answer 21

beautiful

Answer 22

you want me to show a slightly different way you could have done this problem ?

Answer 23

you could have just had one equation
instead of even bothering with the constant of proportionality


that is you could have just solved
\[\frac{\text{ area of second rug }}{\text{ area of first rug }}=\frac{\text{ cost of second rug }}{\text{ cost of first rug }} \\ \frac{x}{324}=\frac{270}{120} \\ \text{ multiply both sides by } 324 \\ x=\frac{270}{120} \cdot 324=729\]

Answer 24

if you didn't like the first way please read that last post

Answer 25

lol I put the costs on the opposite side
but whatever
a=b means b=a
:p