SOLUTION: the sum of two numbers is 105. one-half of one number is equal to one-third of the other number. what are the two numbers? thank u !!! (:

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Question 370991: the sum of two numbers is 105. one-half of one number is equal to one-third of the other number. what are the two numbers?
thank u !!! (:
Found 2 solutions by neatmath, robertb:
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

Let one number be x. The other number is then (105-x).

Then we have:

x%2A%281%2F2%29=%28105-x%29%2A%281%2F3%29 given

6%2Ax%2A%281%2F2%29=6%2A%28105-x%29%2A%281%2F3%29 multiply by 6 on each side to eliminate fractions

3x=2%2A%28105-x%29

3x=210-2x

5x=210

x=42

So if one number is 42, the other number would be 63.

However, we are not quite finished, because we can also set it up this way:

x%2A%281%2F3%29=%28105-x%29%2A%281%2F2%29 given

6%2Ax%2A%281%2F3%29=6%2A%28105-x%29%2A%281%2F2%29 multiply by 6 on each side to eliminate fractions

2x=3%2A%28105-x%29

2x=315-3x

5x=315

x=63

And of course, if one number is 63, the other number must be 42.

This proves that no matter which number you multiply by the fractions of 1/2 and 1/3, you will get the same answer.

In other words, the two numbers will always be 63 and 42.

I hope this helps!

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x = one number
105 - x = other number
Then
x%2F2+=+%28105-x%29%2F3. Cross multiply:
3x = 2(105 - x),or
3x = 210 - 2x,
5x = 210,
x = 42, one number.
105- x = 63, the other number.