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During a special sale, all video games cost $\$21$ and all movies cost $\$14$ . Isabella plans to spend some or all of her $\$140$ in birthday money on these movies and video games. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of video games Isabella can buy $\newline$ $y =$ the number of movies Isabella can buy $\newline$ $\newline$ Choices: $\newline$ (A) 21x + 14y < 140 $\newline$ (B) 14x + 21y < 140 $\newline$ (C) $21x + 14y \leq 140$ $\newline$ (D) $14x + 21y \leq 140$

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Write a linear inequality: word problems

Full solution

Q. During a special sale, all video games cost

\$21

and all movies cost

\$14

. Isabella plans to spend some or all of her

\$140

in birthday money on these movies and video games.

\newline

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

\newline

x =

the number of video games Isabella can buy

\newline

y =

the number of movies Isabella can buy

\newline

\newline

Choices:

\newline

(A)

21x + 14y < 140

\newline

(B)

14x + 21y < 140

\newline

(C)

21x + 14y \leq 140

\newline

(D)

14x + 21y \leq 140

Determine Cost and Budget: Determine the cost per item and the total budget. $\newline$ Isabella's total budget is $\$140$ . The cost of each video game is $\$21$ , and the cost of each movie is $\$14$ . We need to find an inequality that represents the maximum amount she can spend on these items without exceeding her budget.
Define Problem Variables: Define the variables according to the problem. $\newline$ Let $x$ be the number of video games Isabella can buy, and $y$ be the number of movies she can buy. We will use these variables to express the total cost of her purchases.
Write Inequality: Write the inequality that represents the situation. $\newline$ The total cost of the video games is $21x$ dollars, and the total cost of the movies is $14y$ dollars. Since Isabella cannot spend more than her budget of $\$140$ , the sum of these costs must be less than or equal to $\$140$ . Therefore, the inequality is $21x + 14y \leq 140$ .

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