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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) 5x+2=305x + 2 = 30\newline(B) 2x+5=302x + 5 = 30\newline(C) 5(x+2)=305(x + 2) = 30\newline(D) 2(x+5)=302(x + 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) 5x+2=305x + 2 = 30\newline(B) 2x+5=302x + 5 = 30\newline(C) 5(x+2)=305(x + 2) = 30\newline(D) 2(x+5)=302(x + 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 before school and a longer route, xx miles, through his neighborhood after school for 55 days. By the end of the week, he had run a total of 3030 miles. We need to find the value of xx.
  2. Set up the equation: Set up the equation.\newlineSince Russell ran 22 miles before school and xx miles after school each day for 55 days, the total distance run in a week is 55 times the sum of the distances run each day.\newlineThe equation representing this situation is 5(2+x)=305(2 + x) = 30.
  3. Identify the correct equation: Identify the correct equation from the choices.\newlineLooking at the choices given, the correct equation that represents the situation is:\newline(C) 5(x+2)=305(x + 2) = 30
  4. Solve for x: Solve the equation for x.\newlineStarting with the equation 5(x+2)=305(x + 2) = 30, we first distribute the 55:\newline5×x+5×2=305 \times x + 5 \times 2 = 30\newline5x+10=305x + 10 = 30\newlineNow, subtract 1010 from both sides to isolate the term with xx:\newline5x+1010=30105x + 10 - 10 = 30 - 10\newline5x=205x = 20\newlineFinally, divide both sides by 55 to solve for xx:\newline5500\newline5511