Question

Matt bought 7 shirts for a total of $38. Tee shirts cost $5 and long sleeve shirts cost $6. How many of each type of shirt did he buy? HELP PLZ 100 POINTS

Answer 1

tee shirt:4

sleeve shirt:3

Explanation:

we are given two conditions

1. Matt bought 7 shirts for a total of $38
2. Tee shirts cost 5 dollars and long sleeve shirts cost 6 dollars

we want to figure out how many each type of shirt he bought

let tee and sleeve shirts be t and s respectively

according to the first condition

`\displaystyle t + s = 7`

according to the second condition

`\displaystyle5t + 6s = 38`

therefore

our system of linear equation is

`\displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}`

so

now we need our algebra skills to figure out t and s

to do so we can use substitution method

cancel s from both sides of the first equation:

`\displaystyle t = 7 - s \: \cdots \: i`

now substitute the value of i equation to the second equation:

`\displaystyle 5(7 - s) + 6s = 38`

distribute:

`\displaystyle 35 - 5s+ 6s = 38`

collect like terms:

`\displaystyle s + 35 = 38`

cancel 35 to both sides:

`\displaystyle \therefore s = 3`

now substitute the value of s to the i equation:

`\displaystyle t = 7 - 3 \\ \therefore \: t = 4`

hence,

he bought tee shirt 4 and sleeve shirt 3