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you and your go shopping for gift wrap one day. You buy 3 rolls of wrapping paper and 5 bows for a total of $32. Your friend gets 1 roll of wrapping paper and 2 bows for $11. How much does each roll of wrapping paper (x) and each bow (y) cost?

Answer :

Each roll costs $9 and each bow costs $1

3(9) + 5(1)= 32
1(9) + 2(1) = 11

Answer:

Each bow costs $1.

Each roll of wrapping paper costs $9.

Step-by-step explanation:

This question can be solved by a system of equations.

The problem says that:

x is the number of rolls of wrapping paper.

y is the number of bows.

You buy 3 rolls of wrapping paper and 5 bows for a total of $32.

This means that [tex]3x + 5y = 32[/tex].

Your friend gets 1 roll of wrapping paper and 2 bows for $11.

This means that [tex]x + 2y = 11[/tex]. So [tex]x = 11 - 2y[/tex].

Replacing in the first equation.

[tex]3x + 5y = 32[/tex]

[tex]3(11 - 2y) + 5y = 32[/tex]

[tex]-y + 33 = 32[/tex]

[tex]y = 1[/tex]

Each bow costs $1.

[tex]x = 11 - 2y = 11 - 2 = 9[/tex]

Each roll of wrapping paper costs $9.

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