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.

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

2. Solve the system. Find the cost of each item.

Answer 1

The cost of sweatshirt is 12$

Explanation:

so we are going to make 3 equations and solve it using the substation method

First- We know the price of the shirt is two times more so w = 2h

Second we know that the the tee shirt is 4 dollars less then the pair of shoes so t = h − 4

Third we take the combined of Brads purchases 3w + 5t + 2h =136

w = 2h

t = h − 4

3w + 2h + 5t = 136

So to solve we are going to to the sub method

3(2h) + 2h + 5(h-4) = 136 - just re written, now we get rid of the ( )

6h + 2h + 5h -20 = 136 - Now we need to move the -20 and add it too 136

6h + 2h + 5h = 156 - Now sum up the H's

13h = 156 - Now divide 13 by 156

h= 12

so the Cost of a sweatshirt is 12 dollars

Answer 2

The cost of a sweatshirt is $24.

The cost of a t shirt is $8

The cost of shorts is $12

Explanation:

Let w represent the price of one sweatshirt

Let t represent the price of one Tshirt

Let h represent the price of one pair of shorts

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

`w=2h` ...(1)

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

`t=h-4` ....(2)

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

`3w+2h+5t=136` .....(3)

Substituting the values of w and t in (3)

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

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

=>
`13h=136+20`

=>
`13h=156`

h = 12

t = h-4

`t=12-4=8`

t = 8

w = 2h

`w=2*12=24`

w = 24

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So, the cost of a sweatshirt is $24.

The cost of a t shirt is $8

The cost of shorts is $12