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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 clearly: ＂What is the equation to determine the distance between Amy's house and the grocery store?＂
Analyze given information: We know Kamron's house is $0.5$ mile from the grocery store. We also know that Kamron's house is $1.5$ miles closer to the grocery store than Amy's house is. This means that Amy's house is $1.5$ miles further from the grocery store than Kamron's house.
Formulate equation: To find the distance from Amy's house to the grocery store ( $x$ ), we need to add the distance from Kamron's house to the grocery store ( $0.5 ext{ mile}$ ) to the additional distance that Amy's house is from the grocery store ( $1.5 ext{ miles}$ ). So, the equation will be $x = 0.5 + 1.5$ .
Perform calculation: Performing the calculation gives us $x = 2.0$ miles. This means that Amy's house is $2.0$ miles from the grocery store.
Match with options: Now, we need to match our equation with the given options. The correct equation that represents the relationship is $x = 0.5 + 1.5$ , which simplifies to $x = 2.0$ . Looking at the options, the one that matches our equation is (D) $x + 0.5 = 1.5$ , because if we solve for $x$ , we add $0.5$ to both sides to get $x = 2.0$ .

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