Answer:
h=12, w=24, t=8
Step-by-step explanation:
System of Linear Equations
We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.
We have the following data, being
w = price of a sweatshirt
t = price of a T-shirt
h = price of a pair of shorts
19.
The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as
[tex]\displaystyle w=2h[/tex]
The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as
[tex]\displaystyle t=h-4[/tex]
The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus
[tex]\displaystyle 3w+2h+5t=136[/tex]
This is the system of equations we need to solve for w,t,h
20.
To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so
[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]
Operating
[tex]\displaystyle 6h+2h+5h-20=136[/tex]
[tex]\displaystyle 13h=156[/tex]
Solving for h
[tex]\displaystyle h=12[/tex]
The other two variables are
[tex]\displaystyle w=2h=24[/tex]
[tex]\displaystyle t=12-4=8[/tex]
