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=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