Question

Phyllis and Angela are in charge of the office Christmas Party. The theme is "Nutcracker Christmas." Angela purchased 20 nutcrackers and 30 gingerbread cookies for $160. Phyllis went to the same store later and purchased 10 nutcrackers and 25 gingerbread cookies for $100.

A. How much were the gingerbread cookies?
B. How much were the nutcrackers?

Answer 1

The gingerbread cookies cost $2 each, and the nutcrackers cost $5 each. This was determined by formulating and solving a system of linear equations derived from the purchases made by Phyllis and Angela.

Step-by-step explanation:

Phyllis and Angela purchased nutcrackers and gingerbread cookies for their office Christmas Party with a "Nutcracker Christmas" theme, spending different amounts for different quantities of the items. To determine the price of each individual nutcracker and gingerbread cookie, we can set up a system of equations based on the information provided.

System of Equations

Let's denote n as the price of one nutcracker and g as the price of one gingerbread cookie. The following equations can be formulated from the transactions:

1. 20n + 30g = $160 (Angela's purchase)
2. 10n + 25g = $100 (Phyllis's purchase)

Solving these equations simultaneously, multiply the second equation by 2 to align the n terms:

1. 20n + 30g = $160
2. 20n + 50g = $200 (after multiplying by 2)

Subtracting the first equation from the modified second one, we get:

20g = $40

Then, the price of one gingerbread cookie (g) is $40 ÷ 20, which equals $2 per cookie.

To find the price of one nutcracker (n), we substitute the value of g into one of the initial equations:

10n + 25($2) = $100

10n + $50 = $100

10n = $100 - $50

10n = $50

So, the price of one nutcracker (n) is $50 ÷ 10, which equals $5 per nutcracker.