Question

Question #2e901

Answer 1

`color(blue)(S = 7.5)`
`color(blue)(P = 18.5)`

Explanation:

First, convert the word problem into a system of equations:
The variable S stands for the price of one shirt.
The variable P stands for the price of one pair of pants.
`4 S + 3 P = $85.50`
`3S + 5P = $115.00`

Then, solve the system using either substitution or subtraction(I am using subtraction):

`color(blue)"Subtraction":`
1) Choose a variable(I chose S) and multiply both sides of both equations to reach the least common multiple:
`(4 S + 3 P = $85.50)*3 = (12S +9P = 256.5)`
`(3S + 5P = $115.00)*4 = (12S + 20P = 460)`
2) Subtract the equations to eliminate the variable you chose. Solve:
`12S +20P = 460`
`12S + 9P = 256.5`
__-_______
`11P = 203.5`
`color(blue)(P = 18.5)`
3) Plug in to find the other variable:
`4S + 3(18.5) = 85.5`
`4S + 55.5 = 85.5`
`4S = 30`
`color(blue)(S = 7.5)`