SOLUTION: The numbers 320 and 452 have remainders 14 and 10 when divided the same number. The part i am confused here is how we start the equation. Do we Start by putting it into an algeb

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Question 1174874: The numbers 320 and 452 have remainders 14 and 10 when divided the same number.
The part i am confused here is how we start the equation. Do we Start by putting it into an algebraaic equation?
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

The numbers 320 and 452 have remainders 14 and 10 when divided the same number.

Note that your post does not contain a question. Presumably we are supposed to find what that "same number" is....

The given information means 320-14=306 and 452-10=442 are both divisible by the same number.

You could find all the numbers that divide evenly into both 442 and 306 and find the one(s) that satisfy the given conditions. But it is easier to do that kind of thing if we can make the numbers smaller.

Since 442 and 306 are both divisible by the same number, 442-306=136 is too. That is a number that is small enough we can work with it easily. The divisors of 136 are...
1*136
2*68
4*34
8*17

Since the given remainders are 14 and 10, the number we are looking for has to be greater than 14. So the number we are looking for is PROBABLY 17 -- although 34 or even 68 might work.

Checking 17 for the answer....
320/17 = 18 remainder 14
452/17 = 26 remainder 10

Checking 34 as another possibility....
320/34 = 9 remainder 14
452/34 = 13 remainder 10

So both 17 and 34 could be the number we are looking for. So if the question was to find "the number" that gives remainders of 14 and 10, then the problem is flawed because there are at least two such numbers.

We can check 68 also....
320/68 = 4 remainder 48

So 68 is not going to work.

So the two numbers 17 and 34 both satisfy the conditions of the problem.