Question

sixty five percent of a number is 21 less than four fifths of that number. what is the number?

Answer 1

Hi friend!

65% of a number $( \frac{65x}{100} )$
is (= sign)
21 less than (something minus 21)
four-fifths of that number $( \frac{4x}{5} )$

That number refers to the 'x' that I mentioned.
So we get:
$\frac{65x}{100} = \frac{4x}{5} - 21 \\ \\ \frac{13x}{20} = \frac{(4x - 105)}{5} \: (by \: finding \: the \: LCM \: of \: 1 \: and \: 5) \\ \\ 5(13x) = 20(4x - 105) \\ 65x = 80x - 2100 \\ 80x - 65x = 2100 \\ 15x = 2100 \\ x = \frac{2100}{15} \\ x = 140$

There, you've got your answer. Now let's cross check.
$65\% \: of \: 140 = 91 \\ \frac{4}{5} \: of \: 140 = 112 \\ 112 - 21 = 91 \\ \\ LHS = 65\% \: of \: 140 = 91 \\ RHS = (\frac{4}{5} \times 140) \: - 21 = 112 - 21 = 91 \\ LHS = RHS$

Hope you found my answer helpful. Keep Smiling!