Russell has been training for the Emerald Valley Race. The first week he trained, he ran $5$ days and took the same two routes each day. He ran $2$ miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of $30$ miles. $\newline$ Which equation can Russell use to find how many miles, $x$ , he ran each day after school? $\newline$ Choices: $\newline$ (A) $2(x + 5) = 30$ $\newline$ (B) $5(x + 2) = 30$ $\newline$ (C) $5x + 2 = 30$ $\newline$ (D) $2x + 5 = 30$ $\newline$ How many miles did Russell run each day after school? $\newline$ Write your answer as a whole number or a simplified fraction. $\newline$ ____ miles $\newline$

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Grade 7

Solve two-step equations: word problems

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Q. Russell has been training for the Emerald Valley Race. The first week he trained, he ran

5

days and took the same two routes each day. He ran

2

miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of

30

miles.

\newline

Which equation can Russell use to find how many miles,

x

, he ran each day after school?

\newline

Choices:

\newline

(A)

2(x + 5) = 30

\newline

(B)

5(x + 2) = 30

\newline

(C)

5x + 2 = 30

\newline

(D)

2x + 5 = 30

\newline

How many miles did Russell run each day after school?

\newline

Write your answer as a whole number or a simplified fraction.

\newline

____ miles

\newline

Identify Total Miles: Identify the total miles Russell ran each day and the structure of the equation needed. $\newline$ Russell ran $2$ miles around the football field and $x$ miles through his neighborhood each day, for $5$ days. The equation should reflect the total miles run in a week. $\newline$ Calculation: $5$ days $\times$ ( $2$ miles + $x$ miles) = $30$ miles.
Match Derived Equation: Match the derived equation with the given choices. $\newline$ The correct equation from the calculation is $5(2 + x) = 30$ , which matches choice (B) $5(x + 2) = 30$ .
Solve for x: Solve the equation $5(x + 2) = 30$ to find $x$ . $\newline$ Divide both sides by $5$ : $x + 2 = 6$ . $\newline$ Subtract $2$ from both sides: $x = 4$ .