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? Complete by making a table, letting w= the number of white sweatshirts and r= the number of red sweatshirts.
In your table, have three columms:
w = White, r = Red = 30 -w, and C = Cost = 18.95 c + 19.50 r
One of the row entries will result in C = 572.90. That will be the correct answer.
For example:
If w = 20, r = 10 and C = $574. would be one row entry. That is more than 572.90, so there were more of the cheaper shirts sold. Try w = 22.
To find the number of each color sweatshirt sold by Sandy's Sweatshirt Shop, we can set up a system of equations based on the given information.
Let's use the variables:
w = number of white sweatshirts sold
r = number of red sweatshirts sold
Based on the given information, we have the following equations:
1. The total number of sweatshirts sold:
w + r = 30
2. The total revenue from the sale of sweatshirts:
18.95w + 19.50r = 572.90
Now, let's create a table to organize the information:
| | White Sweatshirts | Red Sweatshirts |
|---|------------------|----------------|
| w | | |
| r | | |
We will fill in the values for w and r such that it satisfies the equations.
Let's solve the system of equations using the method of substitution:
From equation 1, we can rewrite it as:
w = 30 - r
Now we substitute this value of w in equation 2:
18.95(30 - r) + 19.50r = 572.90
Distribute and simplify:
568.50 - 18.95r + 19.50r = 572.90
Combine like terms:
0.55r = 4.40
Divide both sides by 0.55 to solve for r:
r = 4.40 / 0.55 = 8
Substitute the value of r back into equation 1 to solve for w:
w + 8 = 30
w = 30 - 8 = 22
Therefore, the shop sold 22 white sweatshirts and 8 red sweatshirts.
Let's update the table with the final values:
| | White Sweatshirts | Red Sweatshirts |
|---|------------------|----------------|
| w | 22 | |
| r | | 8 |