Question

manny is blending a peach ice cream. he mixes together vanilla ice cream, which sells for $6 per contain, and peach ice cream, which sells for $11.50 per contain. how many containers of each should he use if he wants to have 11 container of ice cream that he can sell for $8 each

Answer 1

Let V be the number of containers of vanilla ice cream that Manny uses, and P be the number of peach ice cream containers that Manny needs to obtain 11 containers at a cost of $8 each. Then we can set the following system of equations:

`\begin{gathered} V+P=11, \\ 6V+11.5P=11\cdot8. \end{gathered}`

Solving the first equation for V we get:

`\begin{gathered} V+P-P=11-P, \\ V=11-P\text{.} \end{gathered}`

Substituting the above equation in the first one we get:

`6(11-P)+11.5P=11\cdot8.`

Simplifying the above equation we get:

`\begin{gathered} 66-6P+11.5P=88, \\ 66+5.5P=88. \end{gathered}`

Subtracting 66 from the above equation we get:

`\begin{gathered} 66+5.5P-66=88-66, \\ 5.5P=22. \end{gathered}`

Dividing the above equation by 5.5 we get:

`\begin{gathered} (5.5P)/(5.5)=(22)/(5.5), \\ P=4. \end{gathered}`

Finally, substituting P=4 in V=11-P we get:

`\begin{gathered} V=11-4, \\ V=7. \end{gathered}`

Answer: Manny needs 7 containers of vanilla ice cream and 4 containers of peach ice cream.