Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised
51.50 by selling 8 rolls of solid paper and 15 rolls of printed paper. Find the cost of each type of wrapping paper.
The Correct Answer and Explanation is:
Step 1: Set up variables
Let:
- xxx = cost of one roll of solid wrapping paper (in dollars)
- yyy = cost of one roll of printed wrapping paper (in dollars)
We are told Ben sold:
- 8 rolls of solid paper → worth 8x8x8x
- 15 rolls of printed paper → worth 15y15y15y
Altogether, Ben raised $51.50. So we set up the equation:8x+15y=51.50(1)8x + 15y = 51.50 \tag{1}8x+15y=51.50(1)
Now, we need more information to solve for both xxx and yyy, such as a second equation involving Joel’s sales. But the problem does not mention Joel’s sales or a second equation. So, with only one equation and two variables, we cannot find a unique solution unless one of the costs is known.
Let’s assume that Joel raised the same total amount or used the same pricing. Suppose Joel sold a different combination and raised a certain amount — but since we are not given Joel’s data, we cannot do that. So instead, maybe the problem is missing information, or we’re supposed to assume the prices are whole or common decimal values.
Let’s try possible values:
Assume:
- Solid paper: $2.00 → x=2.00x = 2.00x=2.00
- Printed paper: $2.50 → y=2.50y = 2.50y=2.50
Check:8(2.00)+15(2.50)=16+37.50=53.50≠51.508(2.00) + 15(2.50) = 16 + 37.50 = 53.50 \ne 51.508(2.00)+15(2.50)=16+37.50=53.50=51.50
Try:
- x=1.50x = 1.50x=1.50, y=2.50y = 2.50y=2.50
8(1.50)+15(2.50)=12+37.50=49.50≠51.508(1.50) + 15(2.50) = 12 + 37.50 = 49.50 \ne 51.508(1.50)+15(2.50)=12+37.50=49.50=51.50
Try:
- x=2.00x = 2.00x=2.00, y=2.35y = 2.35y=2.35
8(2.00)+15(2.35)=16+35.25=51.258(2.00) + 15(2.35) = 16 + 35.25 = 51.258(2.00)+15(2.35)=16+35.25=51.25
Try:
- x=2.00x = 2.00x=2.00, y=2.37y = 2.37y=2.37
8(2.00)+15(2.37)=16+35.55=51.558(2.00) + 15(2.37) = 16 + 35.55 = 51.558(2.00)+15(2.37)=16+35.55=51.55
Eventually, try:
- x=2.00x = 2.00x=2.00, y=2.35y = 2.35y=2.35
8x+15y=16+35.25=51.258x + 15y = 16 + 35.25 = 51.258x+15y=16+35.25=51.25
No simple values give us exactly 51.50.
Best approach: Solve algebraically
Let’s assume Joel raised a different amount to give us a second equation. But we don’t have this. Thus:
👉 There is not enough information to find a unique solution unless:
- The price of one of the papers is known, or
- We are given Joel’s sales to form a second equation.
Conclusion:
We cannot determine the cost of each type of wrapping paper with the given information alone. Only one equation with two unknowns was provided.
If additional info is given — such as Joel’s total sales or price of one type — then we could solve the system.
