Question

I already typed this in 2 days ago, but i did not get to see if I had an answer back, can somebody help me to the link, or can help me do the work, I found the answer using the trial and error method, but is there another way to find it without using the trial and error method?

Thanks!

A teacher wants to give each student in his class some candy. He wants everyone to get an equal number of pieces. the teacher has fewer than 85 pieces of candy. If he arranges the pieces in groups of 2, 3, 4 for each student, he will have 1 piece left over. If he uses groups of 5, he will have none left over. How many pieces of candy does he have?

Obviously, the number will end in a 0 or 5 since the number is a multiple of candy. I found the answer to be 25, but I would like to know if there is an easier way to find it.
Thanks again.

Answer 1

There may be an algebraic method.

Here's how I found 25 to be the answer.

I eliminated any number ending in 0 because they are divisible by 2. That left only 75, 65, 55, 45, 35, and 25 to try.