Carlos and Kristin are selling wrapping paper for a school fundraiser. Customers can buy rolls of
plain wrapping paper and rolls of holiday wrapping paper. Carlos sold 6 rolls of plain wrapping
paper and 1 roll of holiday wrapping paper for a total of $62. Kristin sold 3 rolls of plain
wrapping paper and 10 rolls of holiday wrapping paper for a total of $164. Find the cost each of
one roll of plain wrapping paper and one roll of holiday wrapping paper.

Question

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absor201 absor201 · Answer 1 · 2020-01-19T07:27:22+01:00

The cost of one roll of plain wrapping paper is $8 and one roll of holiday wrapping paper is $14.

Step-by-step explanation:

Let,

Cost of one plain wrapping paper = x

Cost of one holiday wrapping paper = y

According to given statement;

6x+y=62 Eqn 1

3x+10y=164 Eqn 2

Multiplying Eqn 2 by 2

[tex]2(3x+10y=164)\\6x+20y=328\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](6x+20y)-(6x+y)=328-62\\6x+20y-6x-y=266\\19y=266[/tex]

Dividing both sides by 19

[tex]\frac{19y}{19}=\frac{266}{19}\\y=14[/tex]

Putting y = 14 in Eqn 1

[tex]6x+14=62\\6x=62-14\\6x=48[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}=\frac{48}{6}\\x=8[/tex]

The cost of one roll of plain wrapping paper is $8 and one roll of holiday wrapping paper is $14.

Keywords: linear equation, elimination method

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