The sum of three numbers is 81. the second number is 4 times the first. the third number is 3 more than the first. what are the three numbers?

Lets try it this way.  3 numbers sum is equal to 81, thus A+B+C = 81.  Now lets go to the next portion of the question. 

The second number is 4 times the first.  
B = 4A
The third number is 3 more than the first
C = 3+A
since we have everything in terms of A lets solve for A. 

A+ 4A+ (3+A) = 81
do some simple math to find A.
A+4A + 3 + A = 81. 
6A + 3 = 81
6A = 81 -3
6A = 78
 A = 13

Now we got A lets solve for B and C. 

B = 4A 
B = 4(13) 
B = 52

C = 3+A
C = 3+13
C = 16

Now lets check our answer
A+B+C  = 81
13+52+16 = 81

The answer is a good luck