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Logan is buying soda and juice for a party and wants to spend no more than $\$44$ . 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) $2x + 3y \leq 44$ $\newline$ (B) 2x + 3y < 44 $\newline$ (C) 3x + 2y < 44 $\newline$ (D) $3x + 2y \leq 44$

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Write two-variable inequalities: word problems

Full solution

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

\$44

. 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)

2x + 3y \leq 44

\newline

(B)

2x + 3y < 44

\newline

(C)

3x + 2y < 44

\newline

(D)

3x + 2y \leq 44

Calculate cost per bottle: Determine the cost per bottle for soda and juice. We are given that soda costs $\$2$ per bottle, which is represented by the variable $x$ , and juice costs $\$3$ per bottle, which is represented by the variable $y$ . Therefore, the total cost for soda is $2x$ and the total cost for juice is $3y$ .
Combine individual costs: Combine the costs to express the total expenditure on soda and juice. The total cost for buying $x$ bottles of soda and $y$ bottles of juice is the sum of the individual costs, which is $2x + 3y$ .
Apply budget constraint: Apply the budget constraint to the total cost. Logan wants to spend no more than $\$44$ on soda and juice. This means that the total cost for soda and juice must be less than or equal to $\$44$ . Therefore, the inequality that represents this situation is $2x + 3y \leq 44$ .

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