Question 907509
We will call the larger of two numbers L and the smaller of the numbers S.
Three times the larger of two numbers is equal to four times the smaller.
This can be written as

3L=4S

The sum of the numbers is 21.
This can be written as L+S= 21

We can plug the equation L+S =21 into 3L=4S either using L= 21-S or S= 21-L.

Let's try L= 21-S

3L=4S
3(21-S)= 4S
63 -3S = 4S
-3S-4S = -63
-7S    = -63
7S     = 63
S      = 9

If S=9, then 3L=4S
             3L= 4(9)
             3L= 36
              L= 12

Check our work
3L= 4S
3(12) = 4 (9) Yes!