MATHEMATICS HIGH SCHOOL

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

Answers

Answer 1

Answer:

Answer:

tee shirt:4

sleeve shirt:3

Step-by-step explanation:

we are given two conditions

Matt bought 7 shirts for a total of $38
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

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

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:

$\displaystyle t = 7 - 3 \n \therefore \: t = 4$

hence,

he bought tee shirt4 and sleeve shirt3

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