What is David’s age now?

Question

Eight years ago Charles was 1 year older than twice David's age then. In eight years, Charles will be 7/6 as old as David will be then. What is David's age now?

(A) 13

(B) 18

(C) 6/5

(D) 10

(E) None of the above

I got (D) 10 as the answer. Is this correct?

Answer 1

Suppose C is Charles' age now and D is David's age now.

First, let's come up with an equation for 8 years ago.

Eight years ago Charles was 1 year older than twice David's age then.

C - 8 = 2(D - 8) + 1

We subtract 8 for both C and D since this is about 8 years ago.

Next, let's come up with an equation for 8 years from today.

In eight years, Charles will be 7/6 as old as David will be then.

C + 8 = (7/6) · (D + 8)

Similar to the previous, we add 8 to both C and D since this is about 8 years from now.

Since we have 2 variables and 2 equations, it is solvable by either substitution or elimination.

This is your choice of preference.

*Please feel free to ask me any question for clarification.