Question

Kim and Daniel are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapper paper. Kim sold 7 rolls of plain wrapping paper and 8 rolls of shiny wrapping paper for a total of $140. Daniel sold 14 rolls of plain wrapping paper and 7 rolls of shiny wrapping paper for a total of $154. Find the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper.

Answer 1

There are two equation:

1) From Kim

2) From Daniel

Let:

x be the cost of rolls of plain wrapping paper

y be the cost of rolls of shiny wrapping paper

Kim:

7x + 8y = 140

Daniel:

14x + 7y = 154

Using elimination method:

(7x + 8y = 140) * -2  (Multiplying the equation by -2)

-14x - 16y = -280

-14x  -16y = -280

14x + 7y = 154

------------------------------

0x - 9y = -126

9y = 126 (Negative sign cancels from both sides)

y = 126 /9

y = 14

The cost of each shiny wrapping paper is $14.

Now solve x, you pick any two equation to solve for x.

7x + 8y = 140

7x + 8(14) = 140 (You know from above y =14)

7x + 112 = 140

7x = 28

x = 28/7

x = 4

The cost of each plain wrapping paper is $4.

Solution: (4,14)