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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) 2x+5=302x + 5 = 30\newline(B) 5(x+2)=305(x + 2) = 30\newline(C) 2(x+5)=302(x + 5) = 30\newline(D) 5x+2=305x + 2 = 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) 2x+5=302x + 5 = 30\newline(B) 5(x+2)=305(x + 2) = 30\newline(C) 2(x+5)=302(x + 5) = 30\newline(D) 5x+2=305x + 2 = 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. Calculate total daily miles: First, let's figure out the total miles Russell ran each day. He ran 22 miles around the football field and xx miles through his neighborhood daily. So, total daily miles = 22 miles + xx miles.
  2. Find total miles for the week: Russell trained for 55 days. Therefore, the total miles for the week is 55 times the daily miles. So, the equation is 5(2+x)=305(2 + x) = 30.
  3. Simplify the equation: Simplify the equation: 10+5x=3010 + 5x = 30.
  4. Solve for x: Solve for x: Subtract 1010 from both sides to get 5x=205x = 20.
  5. Divide to find x: Divide both sides by 55 to find xx: x=205=4x = \frac{20}{5} = 4.