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Kamron's house is $0.5$ mile from the grocery store. If Kamron's house is $1.5$ miles closer to the grocery store than Amy's house is, which of the following can be used to determine $x$ , the distance between Amy's house and the grocery store in miles? $\newline$ Choose $1$ answer: $\newline$ (A) $0.5 \times x=1.5$ $\newline$ (B) $1.5-x=0.5$ $\newline$ (C) $x-1.5=0.5$ $\newline$ (D) $x+0.5=1.5$

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Write exponential functions: word problems

Full solution

Q. Kamron's house is

0.5

mile from the grocery store. If Kamron's house is

1.5

miles closer to the grocery store than Amy's house is, which of the following can be used to determine

x

, the distance between Amy's house and the grocery store in miles?

\newline

Choose

1

answer:

\newline

(A)

0.5 \times x=1.5

\newline

(B)

1.5-x=0.5

\newline

(C)

x-1.5=0.5

\newline

(D)

x+0.5=1.5

Define question prompt: Let's define the question_prompt: What is the equation to determine the distance between Amy's house and the grocery store?
Given information: We know that Kamron's house is $0.5$ mile from the grocery store.
Equation setup: We also know that Kamron's house is $1.5$ miles closer to the grocery store than Amy's house is. This means that the distance from Amy's house to the grocery store is Kamron's distance plus $1.5$ miles.
Simplify equation: Let $x$ represent the distance from Amy's house to the grocery store. Since Kamron's house is $0.5$ mile from the grocery store, and Amy's house is $1.5$ miles further, we can write the equation as $x = 0.5 + 1.5$ .
Find correct option: Simplifying the equation, we get $x = 2.0$ miles. This means that Amy's house is $2.0$ miles from the grocery store.
Find correct option: Simplifying the equation, we get $x = 2.0$ miles. This means that Amy's house is $2.0$ miles from the grocery store.Now, we need to find which of the given options matches our equation. The correct equation is $x = 0.5 + 1.5$ , which simplifies to $x = 2.0$ . Looking at the options, we see that option (D) $x + 0.5 = 1.5$ is the one that matches our equation if we rearrange it to $x = 1.5 - 0.5$ .

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