PLEASE ANSWER FAST: Zoey and her children went into a grocery store where they sell apples for $2 each and bananas for $0.50 each. Zoey has $8 to spend and must buy a minimum of 7 apples and bananas altogether. If x represents the number of apples purchased and y represents the number of bananas purchased, write and solve a system of inequalities graphically and determine one possible solution.

(2,7)

Step-by-step explanation:

Variable Definitions:

x=

x=

\,\,\text{the number of apples}

the number of apples

y=

y=

\,\,\text{the number of bananas}

the number of bananas

\text{\textquotedblleft a minimum of 7 items"}\rightarrow \text{7 or more items}

“a minimum of 7 items"→7 or more items

Use a \ge≥ symbol

Therefore the total number of apples and bananas, x+yx+y, must be greater than or equal to 7:7:

x+y\ge 7

x+y≥7

\text{\textquotedblleft \$8 to spend"}\rightarrow \text{can spend \$8 or less}

“$8 to spend"→can spend $8 or less

Use a \le≤ symbol

One apple costs $2, so xx apples cost 2x.2x. One banana costs $0.50, so yy bananas cost 0.50y.0.50y. The total 2x+0.50y2x+0.50y must be less than or equal to \$8:$8:

2x+0.50y\le 8

2x+0.50y≤8

\text{Solve each inequality for }y\text{:}

Solve each inequality for y:

\begin{aligned}x+y\ge 7\hspace{30px}& 2x+0.50y\le 8 \\[0.8em] y\ge 7-x \hspace{30px}& 0.50y\le 8-2x \\[0.8em] \hspace{30px}& y\le \frac{8-2x}{0.50} \\[0.8em] & y\le 16-4x\end{aligned}

x+y≥7

y≥7−x

2x+0.50y≤8

0.50y≤8−2x

y≤

0.50

8−2x

y≤16−4x

Graph y\ge 7-xy≥7−x by shading up and graph y\le 16-4xy≤16−4x by shading down:

0

the number of apples

the number of bananas

x

y

0

the number of apples

the number of bananas

(2, 7)

Since the point (2, 7(2,7) is inside the double shaded region, one possible solution to the system of inequalities would be:

Zoey could buy 2 apples and 7 bananas.