Detailed solution:
The price of solid paper is $1.75 each
Printed paper is priced at $2.50 each
Information provided:
Ben's total is $43.50 (12 rolls of solid paper and 9 rolls of printed paper)
Joel's total is $51.50 (8 rolls of solid paper and 15 rolls of printed paper)
Let x represent solid paper
Let y represent printed paper
The equations are: 12x + 9y = 43.50
8x + 15y = 51.50
To find x:
8x + 15y = 51.50
Solving for x gives: 8x = 51.50 - 15y
Thus, x = (51.50 - 15y)/8
Next, substitute x:
12x + 9y = 43.50
Replacing x results in: 12(51.50 - 15y)/8 + 9y = 43.50
Which expands to: (618 - 180y)/8 + 9y = 43.50
Multiplying through by 8 yields: 618 - 180y + 72y = 348
Rearranging gives us: -108y = 348 - 618
This simplifies to: -108y = -270
Dividing by -108 results in: y = 2.50
Using the expression for x:
x = (51.50 - 15y)/8
Substituting y, we get: x = (51.50 - 15(2.5))/8
Thus, x = (51.50 - 37.50)/8
This simplifies to: x = 14/8
Final value is: x = 1.75
Verification: x = 1.75; y = 2.5
Substituting into the first equation: 12x + 9y = 43.50
12(1.75) + 9(2.5) = 43.50
Calculating gives: 21 + 22.50 = 43.50
This confirms: 43.50 = 43.50
Substituting into the second equation: 8x + 15y = 51.50
8(1.75) + 15(2.5) = 51.50
Calculating yields: 14 + 37.50 = 51.50
This also confirms: 51.50 = 51.50
