SOLUTION: Gabriella and Jimmy are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Gabriella sold 12 rolls

Question 995629: Gabriella and Jimmy are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Gabriella sold 12 rolls of plain wrapping paper and 7 rolls of holiday wrapping paper for a total of $294. Jimmy sold 9 rolls of plain wrapping paper and 14 rolls of holiday wrapping paper for a total of $378. Find the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper.
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Gabriella and Jimmy are selling wrapping paper for a school fundraiser.
Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper.
Gabriella sold 12 rolls of plain wrapping paper and 7 rolls of holiday wrapping paper for a total of $294.
Jimmy sold 9 rolls of plain wrapping paper and 14 rolls of holiday wrapping paper for a total of $378.
Find the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper.
:
let p = cost of the plain
let h = cost of the holiday
:
Write an equation for each statement
:
"Gabriella sold 12 rolls of plain wrapping paper and 7 rolls of holiday wrapping paper for a total of $294."
12p + 7h = 294
:
"Jimmy sold 9 rolls of plain wrapping paper and 14 rolls of holiday wrapping paper for a total of $378."
9p + 14h = 378
:
Use elimination here. multiply the 1st eq by 2, subtract the 2nd eq
24p + 14h = 588
9p + 14h = 378
-----------------subtraction eliminates h, find p
15p = 210
p = 210/15
p = $14 for roll of plain paper
:
Find h using the 1st original equation
12(14) + 7h = 294
168 + 7h = 294
7h = 294 - 168
7h = 126
h = 126/7
h = $18 for holiday paper
:
:
Check this in the 2nd equation
9(14) + 14(18) =
126 + 252 = 378
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