Question

Ralph is 3 times as old as Sara. In 6 years , Ralph will be only twice as old as Sara will be then. Find Ralph’s age now .

Answer 1

Answer:

Ralph's current age is 18.

Step-by-step explanation:

Let r and s represent the current ages of Ralph and Sara respectively.  Our task here is to determine r, Ralph's age now.

If Ralph is 3 times as old as Sara now, then r = 3s.

Six years from now, Ralph's age will be r + 6 and Sara's will be s + 6.  Ralph will be only twice as old as Sara will be then.  This can be represented algebraically as

r + 6 = 2(s + 6).

We now have the following system of linear equations to solve:

r + 6 = 2s + 12, or r - 2s = 6, and r = 3s (found earlier, see above).

r - 2s = 6

r = 3s

Substituting 3s for r in r - 2s = 6, we get 3s = 2s + 6, or s = 6.  Sara is 6 years old now, meaning that Ralph is 3(6 years), or 18 years old.

Ralph's current age is 18.