The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.

Question

A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68.
Which statement describes the amounts the team charged for wrapping gifts?

The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.
The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

Answer 1

To determine the correct statement about the amounts the team charged for wrapping gifts, we can set up a system of equations based on the information.

Let:

• \( x \) be the charge for a plain gift (no bow)
• \( y \) be the charge for a decorative gift (with a bow)

From the table given, we have the following information:

1. For the first row: \[ 10x + 9y = 47 \]
2. For the second row: \[ 25x + 12y = 86 \]
3. For the third row: \[ 16x + 12y = 68 \]

We'll use the first two rows to solve for \( x \) and \( y \).

From the first equation, we can express \( y \): \[ 9y = 47 - 10x \implies y = \frac{47 - 10x}{9} \]

Now substitute \( y \) in the second equation: \[ 25x + 12\left(\frac{47 - 10x}{9}\right) = 86 \] Multiply through by 9 to eliminate the fraction: \[ 225x + 12(47 - 10x) = 774 \] \[ 225x + 564 - 120x = 774 \] \[ 105x + 564 = 774 \] \[ 105x = 774 - 564 \] \[ 105x = 210 \implies x = 2 \]

Now substitute \( x = 2 \) back into the equation for \( y \): \[ y = \frac{47 - 10(2)}{9} = \frac{47 - 20}{9} = \frac{27}{9} = 3 \]

We find \( x = 2 \) and \( y = 3 \). Thus, the team charged $2 for a plain gift and $3 for a decorative gift.

So the correct statement is: The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.