Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day?
Setup distance ran for the 7 days:
7n + 21 = 70
Solve for n in the equation 7n + 21 = 70
Step 1: Group constants:
We need to group our constants 21 and 70. To do that, we subtract 21 from both sides
7n + 21 - 21 = 70 - 21
Step 2: Cancel 21 on the left side:
7n = 49
Step 3: Divide each side of the equation by 7
7n/7 = 49/7
n = 7
Source
Setup distance ran for the 7 days:
- n
- n + 1
- n + 2
- n + 3
- n + 4
- n + 5
- n + 6
7n + 21 = 70
Solve for n in the equation 7n + 21 = 70
Step 1: Group constants:
We need to group our constants 21 and 70. To do that, we subtract 21 from both sides
7n + 21 - 21 = 70 - 21
Step 2: Cancel 21 on the left side:
7n = 49
Step 3: Divide each side of the equation by 7
7n/7 = 49/7
n = 7
Source