Question 1197889

5/12 of a number is subtracted from 3/4 of the number.Their positive difference is 7 less than 5/6 of the number.Find the number.
<pre>Let the number be N
{{{matrix(3,7, 5/12, of, the, "number:", (5/12)N, or, 5N/12, 3/4, of, the, "number:", (3/4)N, or, 3N/4,  5/6, of, the, "number:", (5/6)N, or, 5N/6)}}} 

We then have: {{{matrix(1,3, 3N/4 - 5N/12, "=", 5N/6 - 7)}}}
              9N - 5N = 10N - 84 ------ Multiplying by LCD, 12
             4N - 10N = - 84
                 - 6N = - 84
         Number or {{{highlight_green(matrix(1,5, N, "=", (- 84)/(- 6), "=", 14))}}}</pre>