During a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. Later you buy three more sweatshirts and four more pairs of sweatpants for $123.00 What is the sale price of each sweatshirt and each pair of sweatpants?
let x = shirts and y = pants
3x + 4y = 123
3x + 2y = 85.5
Subtract second equation from first.
2y = 37.5
Can you carry on from there?
To find the sale price of each sweatshirt and each pair of sweatpants, we can set up a system of equations.
Let's use the variables "s" for the price of each sweatshirt and "p" for the price of each pair of sweatpants.
From the information given, we know that:
3s + 2p = 85.50 (equation 1)
3s + 4p = 123.00 (equation 2)
To solve this system of equations, we can use the method of elimination. By subtracting equation 1 from equation 2, we can eliminate the "s" term:
(3s + 4p) - (3s + 2p) = 123.00 - 85.50
3s - 3s + 4p - 2p = 37.50
2p = 37.50
p = 37.50 / 2
p = 18.75
Now that we have found the price of each pair of sweatpants, we can substitute this value into either equation 1 or equation 2 to find the price of each sweatshirt.
Let's substitute it into equation 1:
3s + 2(18.75) = 85.50
3s + 37.50 = 85.50
3s = 85.50 - 37.50
3s = 48
s = 48 / 3
s = 16
Therefore, the sale price of each sweatshirt is $16, and the sale price of each pair of sweatpants is $18.75.