Question 1111769
Let "s" represent Sylvia's age and "k" represent Kim's age.  Since Sylvia is four times as old as Kim, our first equation is s = 4k.  We also know that the difference between their ages is 24, so our second equation is s - k = 24.

We now have simultaneous equations:

     s = 4k
 s - k = 24

In looking at the second equation, if we add k to both sides, we get
     s = 24 + k

We can use a substitution for s from the above statement into the first equation, that is:

24 + k = 4k

Subtracting k from both sides, we get:
    24 = 3k
Dividing both sides by 3, we get:
     8 = k     that is, Kim is 8 years old.

If Kim is 8 years old, and Sylvia is 4 times as old as Kim, then
     s = 4 * 8 = 32

So, Sylvia is 32 years old.