Question

The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.

19Let w represent the price of one sweatshirt, t represent the price of one T-shirt, and h represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.

20= Solve the system. Find the cost of each item.

Answer 1

Price of sweatshirt = $24

Price of t-shirt=$8

Price of shorts= $12

Explanation:

Let

w be the price of one sweat shirt

t be the price of t-shirt

h be the price of shorts

The first statement is:

The price of a sweatshirt at a local shop is twice the price of a pair of shorts.

w=2h Eqn 1

Then,

The price of a T-shirt at the shop is $4 less than the price of a pair of shorts.

t=h-4 Eqn 2

And

Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.

3w+2h+5t=136 Eqn 3

Putting the value of w and t in equation 3

3w+2h+5t=136

3(2h)+2h+5(h-4)=136

6h+2h+5h-20=136

13h=136+20

h=156/13

h=12

So the price of pair of shorts is $12.

Putting the value of h in equation 1

w=2(12)

w=24

Price of sweatshirt is: $24

Putting the value of h in eqn 2:

t=12-4

t=8

Price of T-shirt is $8 ..