Answer: Khloe could buy 3 bags of popcorn and 9 candies.
Step-by-step explanation:
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of bags of popcorn}
the number of bags of popcorn
y=
y=
\,\,\text{the number of candies}
the number of candies
\text{\textquotedblleft no less than 11 items"}\rightarrow \text{11 or more items}
“no less than 11 items"→11 or more items
Use a \ge≥ symbol
Therefore the total number of bags of popcorn and candies, x+yx+y, must be greater than or equal to 11:11:
x+y\ge 11
x+y≥11
\text{\textquotedblleft \$60 to spend"}\rightarrow \text{can spend \$60 or less}
“$60 to spend"→can spend $60 or less
Use a \le≤ symbol
One bag of popcorn costs $7, so xx bags of popcorn cost 7x.7x. One candy costs $4, so yy candies cost 4y.4y. The total 7x+4y7x+4y must be less than or equal to \$60:$60:
7x+4y\le 60
7x+4y≤60
\text{Solve each inequality for }y\text{:}
Solve each inequality for y:
\begin{aligned}x+y\ge 11\hspace{30px}& 7x+4y\le 60 \\[0.8em] y\ge 11-x \hspace{30px}& 4y\le 60-7x \\[0.8em] \hspace{30px}& y\le \frac{60-7x}{4} \\[0.8em] & y\le 15-\frac{7}{4}x\end{aligned}
x+y≥11
y≥11−x
7x+4y≤60
4y≤60−7x
y≤
4
60−7x
y≤15−
4
7
x
Graph y\ge 11-xy≥11−x by shading up and graph y\le 15-\frac{7}{4}xy≤15−
4
7
x by shading down:
0
the number of bags of popcorn
the number of candies
x
y
0
the number of bags of popcorn
the number of candies
(3, 9)
Since the point (3, 9(3,9) is inside the double shaded region, one possible solution to the system of inequalities would be:
Khloe could buy 3 bags of popcorn and 9 candies.
