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 <
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 <