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

$\begin{gathered} 7.11-0.75y+0.50y=6 \\ 7.11-6=0.75y-0.50y \\ 1.11=0.25y \\ y=\frac{1.11}{0.25} \\ y=4.44 \end{gathered}$

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