Jack and beth are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Jack sold 5 rolls of plain and 8 rolls of shiny for a total of $190. Beth sold of 5 rolls plain and 3 shiny for a total of $90. Find the cost of each roll of wrapping paper

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berno berno · Answer 1 · 2021-02-21T01:26:37+01:00

Answer:

Cost of a roll of plain wrapping paper = $6

Cost of a roll of shiny wrapping paper = $20

Step-by-step explanation:

Let [tex]x[/tex] denotes cost of a roll of plain wrapping paper and [tex]y[/tex] denotes cost of roll of shiny wrapping paper.

Jack sold 5 rolls of plain and 8 rolls of shiny for a total of $190.

[tex]5x+8y=190\,\,\,(i)[/tex]

Beth sold of 5 rolls plain and 3 shiny for a total of $90.

[tex]5x+3y=90\,\,\,(ii)[/tex]

Subtract (ii) from (i).

[tex]8y-3y=190-90\\5y=100\\y=20[/tex]

Put [tex]y=20[/tex] in (ii)

[tex]5x+3(20)=90\\5x+60=90\\5x=90-60\\5x=30\\x=6[/tex]

Therefore,

Cost of a roll of plain wrapping paper = $6

Cost of a roll of shiny wrapping paper = $20