Question

6. Ham sandwiches cost $2.45 and turkey sandwiches cost $2.55. Samantha bought a total of 8 sandwiches for $20.10. How many of each sandwich did she buy? Ham Sandwiches: Turkey Sandwiches:

Answer 1

Let:

x = Number of ham sandwiches

y = Number of turkey sandwiches

Samantha bought a total of 8 sandwiches for $20.10, so:

`\begin{gathered} x+y=8 \\ 2.45x+2.55y=20.10 \end{gathered}`

Let:

`\begin{gathered} x+y=8_{\text{ }}(1) \\ 2.45x+2.55y=20.10_{\text{ }}(2) \\ From_{\text{ }}(1) \\ x=8-y_{\text{ }}(3) \\ Replace_{\text{ }}(3)_{\text{ }}into_{\text{ }}(2) \\ 2.45(8-y)+2.55y=20.10 \\ 19.6-2.45y+2.55y=20.10 \\ 0.1y=0.5 \\ y=(0.5)/(0.1) \\ y=5 \end{gathered}`

Replace the value of y into (3):

`\begin{gathered} x=8-5 \\ x=3 \end{gathered}`

Ham Sandwiches: 3

Turkey Sandwiches: 5