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Omar is buying soda and juice for a party and wants to spend no more than $\$45$ . Soda costs $\$2$ per bottle, and juice costs $\$3$ per bottle. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of bottles of soda $\newline$ $y =$ the number of bottles of juice $\newline$ Choices: $\newline$ (A) $3x + 2y \leq 45$ $\newline$ (B) $2x + 3y \leq 45$ $\newline$ (C) $3x + 2y < 45$ $\newline$ (D) $2x + 3y < 45$

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Write two-variable inequalities: word problems

Full solution

Q. Omar is buying soda and juice for a party and wants to spend no more than

\$45

. Soda costs

\$2

per bottle, and juice costs

\$3

per bottle.

\newline

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

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

Choices:

\newline

(A)

3x + 2y \leq 45

\newline

(B)

2x + 3y \leq 45

\newline

(C)

3x + 2y < 45

\newline

(D)

2x + 3y < 45

Calculate Soda Cost: Soda costs $\$2$ per bottle, so the total cost for soda is $2$ times the number of bottles of soda, which is $2x$ .
Calculate Juice Cost: Juice costs $\$3$ per bottle, so the total cost for juice is $3$ times the number of bottles of juice, which is $3y$ .
Set Spending Limit: Omar wants to spend no more than $\$45$ , so the total cost for soda and juice combined should be less than or equal to $\$45$ .
Combine Costs for Inequality: Adding the cost of soda and juice together gives us the inequality $2x + 3y \leq 45$ .

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