Sergio walked to and from school on 3/5 of the days in one month. He got a ride to school on 7/8 of the remaining days. On the one remaining school day that month he stayed home with a cold. How many school days were there that month?

there were 20 school days that month

Step-by-step explanation:

Let x represent the number of school days that were there that month.

Sergio walked to and from school on 3/5 of the days in one month. This means that the number of days that he walked to and from school is 3x/5

The remaining number of days would be

x - 3x/5 = 2x/5

He got a ride to school on 7/8 of the remaining days. This means that the number of days in which he got a ride to school is

7/8 × 2x/5 = 7x/20

The remaining number of days would be

2x/5 - 7x/20 = (8x - 7x)/20 = x/20

On the one remaining school day that month he stayed home with a cold. This means that

x/20 = 1

x = 20 × 1 = 20