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Eve is celebrating her birthday at a local pizza parlor. The all-you-can-eat meal costs $\$5$ per adult and $\$3$ per child. She wants to stay under a budget of $\$170$ for the party. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of adults attending $\newline$ $y =$ the number of children attending $\newline$ Choices: $\newline$ (A) 5x \cdot 3y < 170 $\newline$ (B) 5x + 3y < 170 $\newline$ (C) $5x - 3y \leq 170$ $\newline$ (D) $5x + 3y \leq 170$

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Write a linear inequality: word problems

Full solution

Q. Eve is celebrating her birthday at a local pizza parlor. The all-you-can-eat meal costs

\$5

per adult and

\$3

per child. She wants to stay under a budget of

\$170

for the party.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of adults attending

\newline

y =

the number of children attending

\newline

Choices:

\newline

(A)

5x \cdot 3y < 170

\newline

(B)

5x + 3y < 170

\newline

(C)

5x - 3y \leq 170

\newline

(D)

5x + 3y \leq 170

Calculate Adult Cost: Determine the cost per adult and the number of adults attending. $\newline$ Cost per adult: $\$5$ $\newline$ Number of adults attending: $x$ $\newline$ What is the total cost for all adults? $\newline$ Cost per adult $\times$ Number of adults attending $\newline$ $= 5 \times x$ $\newline$ $= 5x$ $\newline$ Total cost for adults: $5x$
Calculate Child Cost: Determine the cost per child and the number of children attending. $\newline$ Cost per child: $\$3$ $\newline$ Number of children attending: $y$ $\newline$ What is the total cost for all children? $\newline$ Cost per child $\times$ Number of children attending $\newline$ $= 3 \times y$ $\newline$ $= 3y$ $\newline$ Total cost for children: $3y$
Find Total Party Cost: Combine the total costs for adults and children to find the total cost of the party. $\newline$ Total cost for adults: $5x$ $\newline$ Total cost for children: $3y$ $\newline$ What is the total cost for the party? $\newline$ Add total cost for adults and total cost for children. $\newline$ $5x + 3y$
Compare to Budget: Compare the total cost of the party to Eve's budget. $\newline$ Eve's budget: $\$170$ $\newline$ Total cost of the party: $5x + 3y$ $\newline$ Eve wants to stay under the budget. $\newline$ Select the inequality that describes this situation. $\newline$ Total cost of the party must be less than or equal to the budget. $\newline$ Inequality: $5x + 3y \leq 170$

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