Q:

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?

Accepted Solution

A:
Answer:Sweatshirts cost $16 each Sweatpants cost $18.75 eachStep-by-step explanation:Letprice of sweatshirts be xprice of sweatpants be yFirstly, we can write:3x + 2y = 85.50From the next statement, we can write:3x + 4y = 123Now, 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 = -85.50Then we add this equation to 2nd equation to get:-3x - 2y = -85.503x + 4y = 123--------------------------2y = 37.5y = 37.5/2y = $18.75Now, we plug in this value of y into 2nd equation and solve for x:3x + 4y = 1233x + 4(18.75) = 1233x + 75 = 1233x = 48x = 48/3x = $16Thus,Sweatshirts cost $16 each Sweatpants cost $18.75 each