Khloe and her children went into a movie theater where they sell bags of popcorn for $7 each and candies for $4 each. khope has $60 and must buy no less than 11 bags of popcorn and candies altogether. if x represents the number of bags of popcorn purchased and y represents the number of candies pruchased, write and solve a system of inequalities and determine one possible solution both inequalities must start with y

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.

d

step-by-step explanation:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph