Question

Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.

How many miles did Priya run last week


Elena writes the equation 1/9(x﹣7) = 4 to describe the situation. She solves the equation by multiplying each side by 9 and then adding 7 to each side. How does her solution compare to the way you found Priya’s miles?

Answer 1

1) The number of miles Priya ran last week was 43 miles

2) The way Elena found Priya's miles is faster compared to the way it was found here

Explanation:

1) The number of miles Priya ran this week = The number of miles Priya ran last week - 7

The number of miles Priya ran this week = 9 × The number of miles Elena ran this week

The number of miles Elena ran this week = 4 miles

Therefore;

Let the number of miles Priya ran last week = x miles

The number of miles Priya ran this week = (x - 7) miles

Therefore, we have

(x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles

x = (36 + 7) miles = 43 miles

The number of miles Priya ran last week = x miles = 43 miles

The number of miles Priya ran last week = 43 miles

2) From (x - 7) = 9 × The number of miles Elena ran this week = 9 × 4 miles = 36 miles, we have;

(x - 7) = 9 × 4

1/9(x - 7) = 4

Therefore, multiplying by 9, we have;

9 × 1/9(x - 7) = 9 × 4

(x - 7) = 9 × 4 = 36

x - 7 + 7 = 36 + 7

x = 43 miles

Therefore, the way Elena found Priya's miles is faster compared to the way it is found here