A number is less than 3,000. If you divide this number by 32, the remainder is 30. If you divide the number by 58, the remainder is 44. What's the number?

Question

Please help us solve this 5th grade math problem our daughter was given! We don't see any other solution than plugging specific numbers into an equation with two variables until we get the answer. Are we missing something obvious?

Answer 1

Unless I'm missing something this is a difficult problem for a 5th grader.

Here's my solution.

The number is almost divisible by 58 and almost divisible by 32.

If the remainder is 44 when you divide this number by 58, you should get on your calculator 44/58=0.758620689.

If the remainder is 30 when you divide this number by 32, you should get on your calculator 30/32=0.9375.

That said, find the least common multiple of 58 and 32.

58=2*29

32=2*2*2*2*2

LCM=2*2*2*2*2*29=928

928 is divisible by 58 but if you add 44 to 928 you get 972 which when divided by 58 gives you 16.758620689, which is what you want, 58 R 44

however 972 divided by 32 gives you 30.375 (remember you need to get 0.9375 on your calculator)

add 58 to 972 to get a number which when divided by 58 still leaves a remainder of 44

but 972+58=1030 and 1030 divided by 32 gives 32.1875 (remember you need to get 0.9375 on your calculator)

add another 58 to 1030 to get 1088 and 1088/58=18.758620689

but 1088/32=34

add another 58 to 1088 to get 1146 but 1146/32=35.8125

keep adding 58's to finally get 1726

1726/58=29.758620689 which is 29 remainder 44 (which is what you want)

1726/32=53.9375 which is 53 remainder 30 (which is what you want)

basically you find the LCM of 58 and 32, then add 44, then add 58's (13 of them to be exact) until you get the desired result of 1726