Question

During a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for 85.50. Later you return to the same store and buy three more sweatshirts and four more pairs of sweatpants for $123. What is the sale price of each sweatshirt and each pair of sweatpants?

Answer 1

Sweatshirts cost $16 each

Sweatpants cost $18.75 each

Explanation:

Let

price of sweatshirts be x

price of sweatpants be y

Firstly, we can write:

3x + 2y = 85.50

From the next statement, we can write:

3x + 4y = 123

Now, we need to solve the system of equation for "x" and "y".

First, let's multiply the 1st equation by "-1", so we have:

-1 * [3x+2y=85.50] = -3x - 2y = -85.50

Then we add this equation to 2nd equation to get:

-3x - 2y = -85.50

3x + 4y = 123

--------------------------

2y = 37.5

y = 37.5/2

y = $18.75

Now, we plug in this value of y into 2nd equation and solve for x:

3x + 4y = 123

3x + 4(18.75) = 123

3x + 75 = 123

3x = 48

x = 48/3

x = $16

Thus,

Sweatshirts cost $16 each

Sweatpants cost $18.75 each