How many miles must Mary run during the next week to reach her goal?

Question

Last week Mary ran 6 1/2 miles per day on each of the 7 days. This week Mary ran 8 1/3 miles per day on each of the 5 days. If her goal is to reach a total of 100 miles in three weeks, how many miles must Mary run during the next week to reach her goal?

Answer 1

Last week Mary ran 6 1/2 miles per day on each of the 7 days. This week Mary ran 8 1/3 miles per day on each of the 5 days. If her goal is to reach a total of 100 miles in three weeks, how many miles must Mary run during the next week to reach her goal?

Remember that: (days)*(miles per day) = miles [note: :days cancel out]

You may convert all values from mixed numbers to improper fractions -- OR ... - you may add the integer portions and convert only the fractions. Let's do that (errors are less likely) !

days miles/day miles

Week 1: 7 6 1/2 42 7/2

Week 2: 5 8 1/3 40 5/3

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82 + 7/2 + 5/3

82 + 7/2 + 5/3 = 82 + 21/6 + 10/6 = 82 + 31/6 = 82 + 5 + 1/6 = 87 1/6 miles so far

100 - 87 1/6 = 99 6/6 - 87 1/6 ["borrow" 1]

12 5/6 miles for next week

Answer 2

6 1/2 = 13/2

13/2(7) = 91/2

8 1/3 = 25/3

25/3(5) = 125/3

91/2 + 125/3 = 273/6 + 250/6 = 513/6

100 = 600/6

600/6 - 513/6 = 87/6 = 12 3/6 = 12 1/2 miles