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 !!! (:

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) (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:

given

multiply by 6 on each side to eliminate fractions

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:

given

multiply by 6 on each side to eliminate fractions

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) (Show Source): You can put this solution on YOUR website!
x = one number
105 - x = other number
Then
. Cross multiply:
3x = 2(105 - x),or
3x = 210 - 2x,
5x = 210,
x = 42, one number.
105- x = 63, the other number.
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