To find the ratio, we must find the total amount of days (31) and the number of days that are either a Saturday or a Sunday (10). Since in the sentence, the number of Saturdays and Sundays is mentioned first, the 10 would precede the 31 in the ratio.
1) First figure out the number of days in August. This is easy because it's given to you - it's the number of days on the calendar, 31.
2) Next, count up the number of Saturdays and Sundays. There are 5 Saturdays + 5 Sundays = 10 total.
3) Finally put it as a ratio. Since you're looking for the ratio of "something" to "something," you want to put it as the first thing over the second thing (if in fraction form) or first thing:second thing.
So Saturdays and Sundays to total number of days: or 10:31