Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 36 . How old are they now?

Question

Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 36 . How old are they now?

Answer 1

Hi Kathryn,

Here's how I would think of this problem. Let's call Jack's current age j, and Lacy's current age l. Then we'll write two equations, one for each of the statements in the problem.

1. Jack is 4 times as old as Lacy ⇒ j = 4l
2. 3 years from now the sum of their ages will be 36 ⇒ (j + 3) + (l + 3) = 36

The second equation might need a little bit more explanation. In three years, each of them will have aged by three years. Hence we add three to each of their ages, then add their new ages together to get 36.

Now, as is common with such problems where we have two equations and two unknowns, we first solve one of the equations for one of the variables in terms of the other. In this case, this is already done. Our first equation expresses j in terms of l. So, we can plug that into our second equation

(4l + 3) + (l + 3) = 36

5l + 6 = 36

5l = 30

l = 6

Putting this information back into our first equation yields

j = 4(6) = 24

Thus, Jack's current age is 24 and Lacy's current age is 6. We can check that this makes sense. Jack is indeed 4 times older than Lacy, and in three years, Jack will be 27 and Lacy will be 9. The sum of 27 and 9 is indeed 36, so we have the correct result.

All the best in your studies!

-Joel