Question

Jessica and Riley are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping

paper or holiday wrapping paper. Jessica solf 5 rolls of plain and 13 rolls of holiday wrapping paper for a total
$272. Ryan solf 11 rolls of plain and 16 rolls of holiday wrapping paper for a total $359. What is the cost of one
roll of plain wrapping paper and one roll of holiday wrapping paper?

Answer 1

Cost of one roll of plain wrapping:
`\$5`

Cost of one roll of holiday wrapping paper:
`\$19`

Explanation:

Let be "p" the cost in dollars of one roll of plain wrapping paper and "h" the cost in dollars of one roll of holiday wrapping paper.

Based on the information given, we can set up this system of equations:

`\left \{ {{5p+13h=272} \atop {11p+16h=359}} \right.`

In order to solve it, we can use the Substitution method. The steps are:

1. Solve for "p" from the first equation:

`5p+13h=272\\\\5p=272-13h\\\\p=(272-13h)/(5)`

2. Substitute the above into the second equation and solve for "h":

`11((272-13h)/(5))+16h=359\\\\598.4-28.6h+16h=359\\\\-12.6h=359-598.4\\\\h=(-239.4)/(-12.6)\\\\h=19`

3. Substitute the value of "h" into
`p=(272-13h)/(5)`:

`p=(272-13(19))/(5)\\\\p=5`