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. Which equation can Russell use to find how many miles, x, he ran each day after school? Choices: (A)2x + 5 = 30 (B)2(x + 5) = 30 (C)5x + 2 = 30 (D)5(x + 2) = 30 How many miles did Russell run each day after school? Write your answer as a whole number or a simplified fraction. ____ miles

Question

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. Which equation can Russell use to find how many miles, x, he ran each day after school?   Choices: (A)2x + 5 = 30 (B)2(x + 5) = 30 (C)5x + 2 = 30 (D)5(x + 2) = 30  How many miles did Russell run each day after school? Write your answer as a whole number or a simplified fraction.   ____ miles

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. Russell ran 2 miles around the football field and an unknown distance x through his neighborhood each day for 5 days. The total distance run in the week is 30 miles. We need to find an equation that represents this situation and solve for x.Translate the problem: Translate the problem into an equation. Russell ran 2 miles around the football field each day, so in 5 days, he ran 5 * 2 miles around the football field. He also ran x miles through his neighborhood each day for 5 days, which is 5 * x miles. The sum of these two distances is equal to the total distance run in the week, which is 30 miles. Therefore, the equation is 5 * 2 + 5 * x = 30.Simplify the equation: Simplify the equation. 5 * 2 is 10, so the equation becomes 10 + 5x = 30.Identify the correct equation: Identify the correct equation from the choices. The equation we derived, 10 + 5x = 30, matches choice (C) 5x + 2 = 30 if we rearrange the terms. However, we need to check if we made a mistake because the terms seem to be in the wrong order.Correction: Step 4 (Correction): Identify the correct equation from the choices. The correct equation is 5x + 10 = 30, which is not listed in the choices. However, if we look closely, we can see that choice (D) 5(x + 2) = 30 is equivalent to our equation when the distributive property is applied. Therefore, the correct choice is (D) 5(x + 2) = 30.Solve for x: Solve the equation for x. We have the equation 5(x + 2) = 30. To solve for x, we first divide both sides by 5 to get x + 2 = 6. Then, we subtract 2 from both sides to find x.Perform calculations: Perform the calculations to find x. x + 2 = 6 x = 6 - 2 x = 4

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