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?

Let x=smaller number

Then x+5=larger number

Now we are told the following:

1/5 (x+x+5) = x-5 multiply each side by 5

x+x+5=5x-25 subtract 5x and also 5 from both sides

x+x+5-5-5x=5x-5x-25-5 collect like terms

-3x=-30 divide both sides by - 3

x=10 smaller number

x+5=10+5=15 larger number

CK

1/5 (10+15) = 10-5

1/5 (25) = 10-5

5=5