Question

Desmond has a collection of sports jerseys but cannot remember exactly how many jerseys he has.

When he puts them in piles of 8, there are 4 remaining.



If he puts them in piles of 6, there are 2 remaining. Finally, if he puts them in piles of 5, there are 3 remaining.



If Desmond knows he has fewer than 100 jerseys, how many does he have?

Answer 1

Desmond has 480 jerseys, as it satisfies the conditions when divided into piles of 6.

Step-by-step explanation:

To find out how many jerseys Desmond has, we need to look for a number that satisfies the given conditions. Desmond has a remainder of 4 when the jerseys are divided into piles of 8, a remainder of 2 when divided into piles of 6, and a remainder of 3 when divided into piles of 5. We can start by finding the common multiple of 8, 6, and 5, which is 120. Let's check if this number satisfies the conditions:

1. 120 divided by 8 gives a quotient of 15 with a remainder of 0. Not satisfied.
2. 120 divided by 6 gives a quotient of 20 with a remainder of 0. Not satisfied.
3. 120 divided by 5 gives a quotient of 24 with a remainder of 0. Not satisfied.

Since 120 is not a satisfying number, we can continue to check the multiples of 120. The next multiple is 240:

1. 240 divided by 8 gives a quotient of 30 with a remainder of 0. Not satisfied.
2. 240 divided by 6 gives a quotient of 40 with a remainder of 0. Not satisfied.
3. 240 divided by 5 gives a quotient of 48 with a remainder of 0. Not satisfied.

We can continue this process until we find a number that satisfies all the conditions. Let's try the next multiple of 240, which is 360:

1. 360 divided by 8 gives a quotient of 45 with a remainder of 4. Not satisfied.
2. 360 divided by 6 gives a quotient of 60 with a remainder of 0. Not satisfied.
3. 360 divided by 5 gives a quotient of 72 with a remainder of 0. Not satisfied.

Let's try the next multiple of 360, which is 480:

1. 480 divided by 8 gives a quotient of 60 with a remainder of 0. Not satisfied.
2. 480 divided by 6 gives a quotient of 80 with a remainder of 0. Satisfied!
3. 480 divided by 5 gives a quotient of 96 with a remainder of 0. Not satisfied.

Therefore, Desmond has 480 jerseys, as it satisfies the conditions when divided into piles of 6.