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In order to earn some extra money, Rosa is mowing lawns. She charges $\$13$ to mow a small lawn and $\$24$ to mow a large lawn. She would like to make at least $\$110$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ x = the number of small lawns $\newline$ y = the number of large lawns $\newline$ Choices: $\newline$ (A) $24x + 13y \leq 110$ $\newline$ (B) $13x + 24y \leq 110$ $\newline$ (C) $24x + 13y \geq 110$ $\newline$ (D) $13x + 24y \geq 110$

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Write a linear inequality: word problems

Full solution

Q. In order to earn some extra money, Rosa is mowing lawns. She charges

\$13

to mow a small lawn and

\$24

to mow a large lawn. She would like to make at least

\$110

.

\newline

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

\newline

x = the number of small lawns

\newline

y = the number of large lawns

\newline

Choices:

\newline

(A)

24x + 13y \leq 110

\newline

(B)

13x + 24y \leq 110

\newline

(C)

24x + 13y \geq 110

\newline

(D)

13x + 24y \geq 110

Calculate Small Lawn Total: Rosa charges $\$13$ for a small lawn, so the total from small lawns is $13$ times the number of small lawns mowed. $\newline$ Calculation: $13 \times x = 13x$
Calculate Large Lawn Total: She charges $\$24$ for a large lawn, so the total from large lawns is $24$ times the number of large lawns mowed. $\newline$ Calculation: $24 \times y = 24y$
Total Revenue Inequality: Rosa wants to make at least $\$110$ , so the total money from both small and large lawns should be greater than or equal to $\$110$ . $\newline$ Inequality: $13x + 24y \geq 110$

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