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Mrs. Hong is ordering senior portraits of her son to send to their relatives. A medium photo costs $\$12$ and a large photo costs $\$34$ . She wants to spend less than $\$260$ in total. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of medium photos $\newline$ $y =$ the number of large photos $\newline$ Choices: $\newline$ (A) $34x + 12y < 260$ $\newline$ (B) $12x + 34y \leq 260$ $\newline$ (C) $12x + 34y < 260$ $\newline$ (D) $34x + 12y \leq 260$

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Write two-variable inequalities: word problems

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Q. Mrs. Hong is ordering senior portraits of her son to send to their relatives. A medium photo costs

\$12

and a large photo costs

\$34

. She wants to spend less than

\$260

in total.

\newline

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

\newline

x =

the number of medium photos

\newline

y =

the number of large photos

\newline

Choices:

\newline

(A)

34x + 12y < 260

\newline

(B)

12x + 34y \leq 260

\newline

(C)

12x + 34y < 260

\newline

(D)

34x + 12y \leq 260

Determine cost per photo: Determine the cost per photo type. We know that a medium photo costs $\$12$ and a large photo costs $\$34$ . The number of medium photos is represented by $x$ , and the number of large photos is represented by $y$ . Therefore, the total cost for medium photos is $12x$ and the total cost for large photos is $34y$ .
Combine total costs: Combine the costs to represent the total spending on photos. To find the total cost for both medium and large photos, we add the total cost for medium photos to the total cost for large photos, which gives us $12x + 34y$ .
Apply budget constraint: Apply the budget constraint to the total cost. Mrs. Hong wants to spend less than $\$260$ in total on the photos. This means that the combined cost of medium and large photos must be less than $\$260$ . Therefore, the inequality that describes this situation is $12x + 34y < 260$ .
Match to choices: Match the derived inequality to the given choices. The correct inequality that we have found is $12x + 34y < 260$ , which corresponds to choice $(C)$ .

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