Sandy’s Sweatshirt Shop sells
college sweatshirts. White
sweatshirts sell for $18.95 each
and red ones sell for $19.50
each. If receipts for the sale of
30 sweatshirts total $572.90,
how many of each color did the
shop sell?
You can set up a system of equations. Let's make x = white sweatshirts and y = red ones. 18.95x + 19.50y = 572.90 and x + y = 30
Use elimination and go from there.
To solve this problem, let's assume the number of white sweatshirts sold as 'x' and the number of red sweatshirts sold as 'y'.
We have two equations based on the information given:
1. The total number of sweatshirts sold: x + y = 30
2. The total revenue from the sales: 18.95x + 19.50y = 572.90
Now we can solve this system of equations to find the values of x and y.
We can start by multiplying the first equation by 18.95:
18.95(x + y) = 18.95(30)
18.95x + 18.95y = 568.50
Now we can subtract the second equation (18.95x + 18.95y = 568.50) from the third equation (18.95x + 19.50y = 572.90) to eliminate 'x':
(18.95x + 19.50y) - (18.95x + 18.95y) = 572.90 - 568.50
0.55y = 4.40
Divide both sides of the equation by 0.55 to solve for 'y':
y = 4.40 / 0.55
y = 8
Now we can substitute the value of 'y' back into the first equation to solve for 'x':
x + 8 = 30
x = 30 - 8
x = 22
Therefore, the shop sold 22 white sweatshirts and 8 red sweatshirts.