serio 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 remaining school day that month he stayed home with a cold. How many school days were there that month?
3/5 d + [7/8 (2/5 d)] + 1 = d
3/5 d + 7/20 d + 1 = d
12/20 d + 7/20 d + 1 = d
To find the number of school days that month, we can follow these steps:
Step 1: Calculate the fraction of days Serio walked to and from school.
Since he walked on 3/5 of the days, this means he walked on (3/5) * 30 days = 18 days.
Step 2: Calculate the fraction of days Serio didn't walk or stay home (i.e., the remaining school days).
To do this, we subtract the days he walked and the day he stayed home from the total number of days in a month.
Total number of days = 30 days
Remaining days = 30 days - 18 days - 1 day (for staying home with a cold) = 11 days.
Step 3: Calculate the fraction of days Serio got a ride to school.
Since he got a ride on 7/8 of the remaining days, this means he got a ride on (7/8) * 11 days = 77/8 days = 9 days (rounded to the nearest whole number).
Step 4: Calculate the total number of school days.
To find the total number of school days, we add the days Serio walked, got a ride, and stayed home.
Total school days = days walked + days got a ride + days stayed home
Total school days = 18 days + 9 days + 1 day (for staying home with a cold)
Total school days = 28 days.
Therefore, there were 28 school days that month.