Karen ran 42 miles in 6 days. On Sunday she ran 12 miles. Each of the other days she ran the same distance.
1. Write an algebraic equation to show how far Karen ran.
2. Calculate how many miles Karen ran each day for the week.
3. Explain how you arrived at this?
If she ran x miles on 5 of the days, then we have
5x+12 = 42
1. To write an algebraic equation to show how far Karen ran, let's assume that she ran x miles on each of the other days (excluding Sunday). The equation can be written as:
12 + x + x + x + x + x + x = 42
2. To calculate how many miles Karen ran each day for the week, we can solve the above equation.
12 + 5x = 42
Subtracting 12 from both sides:
5x = 30
Dividing both sides by 5:
x = 6
So, Karen ran 6 miles each day (excluding Sunday) for the week.
3. To arrive at this solution, we started by writing an algebraic equation to represent the problem. We assigned the variable x to represent the distance Karen ran on each of the other days. We added up all the distances (12 miles on Sunday and x miles on the remaining five days) to equal the total distance of 42 miles. By solving the equation, we found that x is equal to 6, indicating that Karen ran 6 miles each day (excluding Sunday) for the week.