how many dimes does penny have

Question

Pennys favorite coin is the dime, she doesn't know how many she has but he does know that he has fewer than 100 one day he was arranging them in different ways she found that when she puts them in piles of two there was one left over when she put them into piles of three there was one left over and the same thing happened when she put them in the piles for she then tried putting them in the piles of five and found that there were none left over how many dimes does she have?

Answer 1

Because the dimes AREN'T evenly divisible by 2, there is an odd number of dimes.

Because they ARE evenly divisible by 5, the number of dimes is a multiple of 5.

 

That means, that number of times is less than 100, and ends in 5 (as all odd multiples of 5 do.)

 

Now, start with numbers that follow this criteria and guess and check. Since the scenarios for 2 and 5 are taken care of, we just need to make sure when divided by three, one remains, and when divided by four, one remains.

 

For example: 5 divided by 4 has a remainder of 1, but 5 divided by 3 has a remainder of 2, so the solution can't be 5.

 

The answer is: 25 or 85