SOLUTION: One – third of a number of two digits is greater than one – fourth of its successor by 1 . Find the number .

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Question 879160: One – third of a number of two digits is greater than one – fourth
of its successor by 1 . Find the number .
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
number of two digits = x
one-third of that number = expr%281%2F3%29x

successor of that number = x+1

one-fourth of successor of that number = expr%281%2F4%29%28x%2B1%29


One – third of a number of two digits is greater than one – fourth
of its successor by 1 . Find the number .

Replace the underlined words by expr%281%2F3%29x

expr%281%2F3%29x is greater than one – fourth of its successor by 1 . Find the number .

Replace the underlined words by expr%281%2F4%29%28x%2B1%29

expr%281%2F3%29x is greater than expr%281%2F4%29%28x%2B1%29 by 1 . Find the number .

Mentally translate this by reasoning

If a first thing is greater than a second thing by ONE, that means that the
the first thing equals the second thing PLUS ONE.  So

expr%281%2F3%29x%22%22=%22%22expr%281%2F4%29%28x%2B1%29%2B1

Multiply through by red%2812%29

red%2812%29expr%281%2F3%29x%22%22=%22%22red%2812%29expr%281%2F4%29%28x%2B1%29%2Bred%2812%291

4x = 3(x + 1) + 12
4x = 3x + 3 + 12
4x = 3x + 15
 x = 15

Turns out that they didn't need to tell us that it has two digits.

Checking:

One – third of 15, which is 5, is greater than one – fourth
of (15's) successor 16, (which is 4), by 1.  It's true that
5 is indeed greater than 4 by 1, so we have the correct 
answer, 15.

Edwin