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Russell has been training for the Emerald Valley Race. The first week he trained, he ran 55 days and took the same two routes each day. He ran 22 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 3030 miles.\newlineWhich equation can Russell use to find how many miles, xx, he ran each day after school?\newlineChoices:\newline(A) 5(x+2)=305(x + 2) = 30\newline(B) 5x+2=305x + 2 = 30\newline(C) 2(x+5)=302(x + 5) = 30\newline(D) 2x+5=302x + 5 = 30\newlineHow many miles did Russell run each day after school?\newlineWrite your answer as a whole number or a simplified fraction.\newline____ miles\newline

Full solution

Q. Russell has been training for the Emerald Valley Race. The first week he trained, he ran 55 days and took the same two routes each day. He ran 22 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 3030 miles.\newlineWhich equation can Russell use to find how many miles, xx, he ran each day after school?\newlineChoices:\newline(A) 5(x+2)=305(x + 2) = 30\newline(B) 5x+2=305x + 2 = 30\newline(C) 2(x+5)=302(x + 5) = 30\newline(D) 2x+5=302x + 5 = 30\newlineHow many miles did Russell run each day after school?\newlineWrite your answer as a whole number or a simplified fraction.\newline____ miles\newline
  1. Understand the problem: Understand the problem.\newlineRussell ran 22 miles around the football field and an unknown distance xx through his neighborhood each day for 55 days. The total distance run in the week is 3030 miles. We need to find the value of xx.
  2. Set up the equation: Set up the equation.\newlineRussell ran 22 miles around the football field and xx miles through his neighborhood each day. Since he ran these distances for 55 days, the total distance run for the week is 55 times the sum of the distances run each day.\newlineThe equation is 5(x+2)=305(x + 2) = 30.
  3. Choose the correct equation: Choose the correct equation from the choices.\newlineThe correct equation that represents the situation is (A)5(x+2)=30(A) 5(x + 2) = 30.
  4. Solve the equation for x: Solve the equation for x.\newline5(x+2)=305(x + 2) = 30\newlineDivide both sides by 55 to isolate the term with xx.\newline(x+2)=305(x + 2) = \frac{30}{5}\newline(x+2)=6(x + 2) = 6\newlineSubtract 22 from both sides to solve for xx.\newlinex=62x = 6 - 2\newlinex=4x = 4