Question

Jamie volunteers at the pet shelter every 3 days and at the food pantry every 5 days. For the month of February 2022 the volunteers at the pet shelter on the 3rd day of the month and at the food pantry on the 5th day of the month. When will Jaime volunteer again at both places on the same day?

Answer 1

Jamie will volunteer at the pet shelter and food pantry on the same day on February 15, 2022, as it is the first common multiple of their separate volunteering frequencies after their starting points.

Step-by-step explanation:

Jamie volunteers at the pet shelter every 3 days and at the food pantry every 5 days. The question asks when Jamie will volunteer again at both places on the same day after starting on the 3rd and 5th of February respectively. To find the answer, we need to calculate the Least Common Multiple (LCM) of 3 and 5.

LCM of 3 and 5 is 15 because 15 is the smallest number that both 3 and 5 will divide into without leaving a remainder.

Since Jamie starts volunteering on different days, we must find the first common multiple after their starting points. Jamie first volunteers at the pet shelter on the 3rd and again on every multiple of 3 (6th, 9th, 12th, 15th, ...), and at the food pantry on the 5th and every multiple of 5 (10th, 15th, 20th, 25th, ...).

The first day they will volunteer at both places, considering their initial volunteering dates in February, is February 15, 2022.

Answer 2

Jaime will volunteer at both the pet shelter and the food pantry on the same day by finding the Least Common Multiple (LCM) of 3 and 5, which is 15. Therefore, Jaime's next simultaneous volunteering day is on the 20th of February 2022.

Step-by-step explanation:

To determine when Jaime will volunteer at both the pet shelter and the food pantry on the same day, we need to find the Least Common Multiple (LCM) of the two frequencies of volunteering - every 3 days and every 5 days. First, Jaime volunteers at the pet shelter on the 3rd of February, which means that subsequent volunteering days at the shelter fall on days that are multiples of 3 (6th, 9th, 12th, etc.). Similarly, Jaime volunteers at the food pantry on the 5th of February, meaning that these volunteering days are multiples of 5 (10th, 15th, 20th, etc.).

The LCM of 3 and 5 is 15, which tells us that Jaime will volunteer at both places on the same day every 15 days. Considering that February starts on a day when Jamie volunteers at the pet shelter on the 3rd and at the food pantry on the 5th, the first day they volunteer at both places will be 15 days after the latter of these two dates. Thus, 5 + 15 = 20. Jaime will next volunteer at both locations on the same day on the 20th of February 2022.