Question

In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old are they now?

If x + 5 is Jill's age five years from now, which of the following equations could be used to solve the problem?

3x + 5 = 55 - x
3x + 15 = 55 - x
3x + 15 = 45 - x

Answer 1

Let x be the daughter's age and y be the dad's:
$$
y + x = 50 \implies y = 50 - x \\
y + 5 = 3(x+5) \implies (50-x) + 5 = 3(x+5)\\
55 - x = 3x + 15 \implies 3x + 15 = 55 - x
$$

Answer 2

\[
3x + 15 = 55 - x \implies 4x = 40 \implies x = 10 \\
y = 50 - x \implies y = 50 - 10 = 40
\]