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An animal shelter had 12 fewer cats than their capacity. Then they received 18 stray cats. They need families to adopt some cats right away to get back to their capacity.
Which of the following equations matches the situation above?
Choose 1 answer:
(A)
-12-18+?=0
(B)
12-18-?=0
(C)
-12+18-?=0

An animal shelter had $12$ fewer cats than their capacity. Then they received $18$ stray cats. They need families to adopt some cats right away to get back to their capacity. $\newline$ Which of the following equations matches the situation above? $\newline$ Choose $1$ answer: $\newline$ (A) $-12-18+?=0$ $\newline$ (B) $12-18-?=0$ $\newline$ (C) $-12+18-?=0$

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Write a linear inequality: word problems

Full solution

Q. An animal shelter had

12

fewer cats than their capacity. Then they received

18

stray cats. They need families to adopt some cats right away to get back to their capacity.

\newline

Which of the following equations matches the situation above?

\newline

Choose

1

answer:

\newline

(A)

-12-18+?=0

\newline

(B)

12-18-?=0

\newline

(C)

-12+18-?=0

Define Variables: Let's define the variables: $\newline$ - Let $c$ be the capacity of the shelter. $\newline$ - Let $x$ be the number of cats that need to be adopted to get back to capacity. $\newline$ The shelter had $12$ fewer cats than their capacity, so they had $c - 12$ cats. $\newline$ Then they received $18$ stray cats, so the number of cats increased to $(c - 12) + 18$ . $\newline$ To get back to their capacity, they need to have $c$ cats again. $\newline$ So the equation that represents the situation is: $\newline$ $(c - 12) + 18 - x = c$ $\newline$ Now let's simplify the equation: $\newline$ $c - 12 + 18 - x = c$ $\newline$ $c + 6 - x = c$ $\newline$ Since we want to find the number of cats that need to be adopted to get back to capacity, we can subtract $c$ from both sides of the equation to isolate $x$ : $\newline$ $x$ $2$ $\newline$ $x$ $3$ $\newline$ Now we can rewrite the equation to match the answer choices: $\newline$ $x$ $4$ $\newline$ Multiplying both sides by $x$ $5$ to solve for $x$ , we get: $\newline$ $x$ $7$ $\newline$ This means that $x$ $8$ cats need to be adopted to get back to the shelter's capacity. $\newline$ The equation that matches this situation is: $\newline$ $x$ $9$ which simplifies to $x$ $3$ . $\newline$ So the correct answer is (C) $x$ $9$ .

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