Question

Lydia and her children went into a grocery store where they sell apples for $0.75 eachand peaches for $0.50 each. Lydia has $6 to spend and must buy a minimum of 9apples and peaches altogether. If x represents the number of apples purchased and yrepresents the number of peaches purchased, write and solve a system of inequalitiesgraphically and determine one possible solution.

Answer 1

So first we need to represent our problem with the restriction we have.

`0.75x+0.50y=6`

and the other restriction is:

`x+y=9`

from the second equation we can solve for x, and it will be:

`x=9-y`

and replace that into the first equation:

`0.75(9-y)+0.50y=6`

and now we solve for y

`\begin{gathered} 7.11-0.75y+0.50y=6 \\ 7.11-6=0.75y-0.50y \\ 1.11=0.25y \\ y=(1.11)/(0.25) \\ y=4.44 \end{gathered}`

with this solution we can solve the second equation:

`\begin{gathered} x+4.44=9 \\ x=9-4.44 \\ x=4.56 \end{gathered}`

This is one of the posible solution, now you can play with the decimals, so for example 4 peaches and 6 apples, or 6 peaches and 4 apples