Question

Need some help with these problems!

Answer 1

h=12, w=24, t=8

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

`\displaystyle w=2h`

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

`\displaystyle t=h-4`

The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus

`\displaystyle 3w+2h+5t=136`

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

`\displaystyle 3(2h)+2h+5(h-4)=136`

Operating

`\displaystyle 6h+2h+5h-20=136`

`\displaystyle 13h=156`

Solving for h

`\displaystyle h=12`

The other two variables are

`\displaystyle w=2h=24`

`\displaystyle t=12-4=8`