Question 879160
<pre>
number of two digits = x
one-third of that number = {{{expr(1/3)x}}}

successor of that number = x+1

one-fourth of successor of that number = {{{expr(1/4)(x+1)}}}


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

Replace the underlined words by {{{expr(1/3)x}}}

{{{expr(1/3)x}}} is greater than <u>one – fourth of its successor</u> by 1 . Find the number .

Replace the underlined words by {{{expr(1/4)(x+1)}}}

{{{expr(1/3)x}}} is greater than {{{expr(1/4)(x+1)}}} 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(1/3)x}}}{{{""=""}}}{{{expr(1/4)(x+1)+1}}}

Multiply through by {{{red(12)}}}

{{{red(12)expr(1/3)x}}}{{{""=""}}}{{{red(12)expr(1/4)(x+1)+red(12)1}}}

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</pre>