Question

Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?

Answer 1

Step 1

Michael spends $18 at store A

He buys x pounds of turkey and y pounds of ham.

But turkey costs $3 in-store A and ham costs $4 in-store A

Therefore, we will have the following equation for Michael

`3x+4y=18---(1)`

Step 2

Ashley spends $27 in-store B

She buys x pounds of turkey and y pounds of ham.

But turkey costs $4.50 in-store B and ham costs $6 in-store B.

Therefore, we will have the following equation for Ashley

`4.5x+6y=27----(2)`

Step 3

Solve the equations graphically

If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.

For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.

`\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}`
`\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}`

Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.