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
[tex] \displaystyle t + s = 7[/tex]
according to the second condition
[tex] \displaystyle5t + 6s = 38[/tex]
therefore
our system of linear equation is
[tex] \displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}[/tex]
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:
[tex] \displaystyle t = 7 - s \: \cdots \: i[/tex]
now substitute the value of i equation to the second equation:
[tex] \displaystyle 5(7 - s) + 6s = 38[/tex]
distribute:
[tex] \displaystyle 35 - 5s+ 6s = 38[/tex]
collect like terms:
[tex] \displaystyle s + 35 = 38[/tex]
cancel 35 to both sides:
[tex] \displaystyle \therefore s = 3[/tex]
now substitute the value of s to the i equation:
[tex] \displaystyle t = 7 - 3 \\ \therefore \: t = 4[/tex]
hence,
he bought tee shirt 4 and sleeve shirt 3
