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?
a.3x + 5 = 55 - x
b.3x + 15 = 55 - x
c.3x + 15 = 45 - x ...?

Answer 1

The answer is b.3x + 15 = 55 - x

x - Jill's present age
y - dad's present age

In 5 years, Dad will be three times as old as his daughter Jill will be then:
y + 5 = 3(x + 5)

The sum of their present ages is 50:
x + y = 50

We have the system of two equations now:
y + 5 = 3(x + 5)
x + y = 50

Let's rearrange the second equation:
If: x + y = 50
Then: y = 50 - x

Now, substitute y from the second equation (y = 50 - x) into the first one:
y + 5 = 3(x + 5)
50 - x + 5 = 3(x + 5)
50 + 5 - x = 3*x + 3*5
55 - x = 3x + 15

Rearrange it a bit:
3x + 15 = 55 - x
Therefore, the correct choice is b.