Given the system of equations:
[tex]\begin{cases}4x+2y={30} \\ 2x+3y={21}\end{cases}[/tex]
From the first equation, we have:
[tex]\begin{gathered} 2y=30-4x \\ \Rightarrow y=15-2x \end{gathered}[/tex]
Using this result on the second equation:
[tex]\begin{gathered} 2x+3(15-2x)=21 \\ 2x+45-6x=21 \\ -4x=-24 \\ \Rightarrow x=6 \end{gathered}[/tex]
Then, the cost of 1 wrapping paper is $6.
We use this result to find y:
[tex]\begin{gathered} y=15-2\cdot6 \\ \Rightarrow y=3 \end{gathered}[/tex]
The cost of 1 greeting card is $3.
Part A:
The total cost of 1 wrapping paper and 1 box of greeting cards is:
[tex]x+y=6+3=9[/tex]
Answer: $9
Part B:
The order C is given by:
[tex]4x+4y=4\cdot6+4\cdot3=24+12=36[/tex]
The total cost of order C is $36
