i dont know how to set up the equations
Since the sum of the two numbers is 21,
let x be one number and 21-x be the other.
x + (21-x) = 21
Since "three times the larger of two numbers is equal to four times the smaller"...
3x = 4(21-x)
3x = 84 -4x
7x = 84
x = 12
Since x = 12, 21-x = 21-12 = 9.
Larger number is 12, smaller number is 9.
Note that if you said:
3(21-x) = 4x
63 - 3x = 4x
63 = 7x
x = 9, and 21-x = 21-9 = 12
12 would still be the larger number and 9 would still be the smaller.