Question

The sum of two numbers is 51. If one fourth of one number exceeds one fifth of another number by 6, which of the following is the smaller number?

Answer 1

Let x = 1st number and y = 2nd number
Using the sentences:
The sum of two numbers is 51:  x + y = 51
one fourth of one number exceeds one fifth of another number by 6:
(1/4)x > (1/5)y + 6

This means y is the smaller number.
From x + y = 51 → x = 51 - y
Plug into the inequality
(1/4)(51 - y) > (1/5) y + 6
Multiply each side by 20
5(51 - y) > 4y + 120
251 - 5y > 4y + 120 
-9y > -131
y < $\frac{131}{9}$