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Trent is inviting people to his parents' anniversary party and wants to stay at or below his budget of $\$3,800$ for the food. The cost will be $\$34$ for each adult's meal and $\$22$ for each child's meal. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of adults $\newline$ $y =$ the number of children $\newline$ $\newline$ Choices: $\newline$ (A) $22x + 34y \leq 3,800$ $\newline$ (B) $34 + x + 22 + y \leq 3,800$ $\newline$ (C) $34x + 22y \leq 3,800$ $\newline$ (D) $22 + x + 34 + y \leq 3,800$

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Write a linear inequality: word problems

Full solution

Q. Trent is inviting people to his parents' anniversary party and wants to stay at or below his budget of

\$3,800

for the food. The cost will be

\$34

for each adult's meal and

\$22

for each child's meal.

\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

\newline

y =

the number of children

\newline

\newline

Choices:

\newline

(A)

22x + 34y \leq 3,800

\newline

(B)

34 + x + 22 + y \leq 3,800

\newline

(C)

34x + 22y \leq 3,800

\newline

(D)

22 + x + 34 + y \leq 3,800

Calculate Cost per Child: Determine the cost per child and the number of children. $\newline$ Cost per child meal: $\$22$ $\newline$ Number of children: $y$ $\newline$ What is the total cost for the child meals? $\newline$ Cost per child meal $\times$ Number of children $\newline$ $= 22 \times y$ $\newline$ $= 22y$ $\newline$ Total cost for child meals: $22y$
Find Total Cost: Combine the total costs for adults and children to find the total cost for the party. $\newline$ Total cost for adult meals: $34x$ $\newline$ Total cost for child meals: $22y$ $\newline$ What is the total cost for the party? $\newline$ Add total cost for adult meals and total cost for child meals. $\newline$ $34x + 22y$
Compare with Budget: Compare the total cost with Trent's budget. $\newline$ Trent's budget: $\$3,800$ $\newline$ Total cost for the party: $34x + 22y$ $\newline$ Trent wants to stay at or below his budget. $\newline$ Select the inequality that describes this situation. $\newline$ Total cost must be less than or equal to the budget. $\newline$ Inequality: $34x + 22y \leq 3,800$

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