Question

6. Haley bought three bars of soap and five

sponges for $22. Yesenia bought five bars of
soap and three sponges for $26. Find the cost
of each item

Answer 1

Each soap costs $4.00, while each sponge costs $2.00.

Our two equations are:

3x + 5y = 22
5x + 3y = 26

x = cost of each soap
y = cost of each sponge

Now we solve:

-3(3x + 5y = 22) = -9x- 15y = -66
5(5x + 3y = 26) = 25x + 15y = 130

Our new equations:

-9x- 15y = -66
25x + 15y = 130

16x = 64
/16 /16
x = 4 (each soap costs $4.00)


Now we substitute x into one on our ORIGINAL equations.

3x + 5y = 22
3(4) + 5y = 22
12 + 5y = 22
-12 -12
5y = 10
/5 /5
y = 2 (each sponge costs $2.00)


To check:
3x + 5y = 22
3(4) + 5(2) = 22
12 + 10 = 22
22 = 22
This statement is TRUE, which also makes our answers true.

Hope that helps!