Question

Thetotal cost of orders A and B are given.Part A. What is the total cost of 1 wrapping paper and 1 box of greeting cards?Part B. What is the total cost, in dollars, of order C? $

Answer 1

Given the system of equations:

`\begin{cases}4x+2y={30} \\ 2x+3y={21}\end{cases}`

From the first equation, we have:

`\begin{gathered} 2y=30-4x \\ \Rightarrow y=15-2x \end{gathered}`

Using this result on the second equation:

`\begin{gathered} 2x+3(15-2x)=21 \\ 2x+45-6x=21 \\ -4x=-24 \\ \Rightarrow x=6 \end{gathered}`

Then, the cost of 1 wrapping paper is $6.

We use this result to find y:

`\begin{gathered} y=15-2\cdot6 \\ \Rightarrow y=3 \end{gathered}`

The cost of 1 greeting card is $3.

Part A:

The total cost of 1 wrapping paper and 1 box of greeting cards is:

`x+y=6+3=9`

Answer: $9

Part B:

The order C is given by:

`4x+4y=4\cdot6+4\cdot3=24+12=36`

The total cost of order C is $36