Question

The recycling trucks pick up plastic from the collection bin every three days and glass everyfive days. Suppose both items are picked up today. In how many days will both items again bepicked up on the same day? Write an explanation of how you solved the problem.2) Suppose both items are picked up on a Sunday. How many Mondays will pass before thepickup is on a Monday again?

Answer 1

The recycling trucks will pick up both items together again in 15 days. As 15 days from a Sunday is another Sunday, two Mondays will pass before the pickup is on a Monday again.

Step-by-step explanation:

To find out in how many days both items will be picked up on the same day, we need to find the least common multiple (LCM) of the two pickup intervals: every three days for plastic and every five days for glass. The LCM of 3 and 5 is 15, which is the first number that both 3 and 5 divide into without any remainder. Therefore, in 15 days, both items will again be picked up on the same day.

To determine how many Mondays will pass before the pickup is on a Monday again, we must note that 15 days from any given Sunday is not a Monday; it's a Sunday. Therefore, we need to find the next multiple of 7 (the number of days in a week) that is greater than 15, which is 21. Thus, two Mondays will pass before the pickup is on a Monday again.