On 's birthday, his brother Harry is seventeen years younger

Question

than three times 's age. The boys father, Tom, is twelve years
older than twice Harry's age. If is seven years younger than
his brother, how many candles are on 's cake?

Answer 1

Let D be 's age and H be Harry's age. We have the following equations:

1) H = 3D - 17 (Harry is 17 years younger than three times 's age)
2) D = H - 7 ( is 7 years younger than Harry)

First, we solve equation 2 for H: H = D + 7.

Now we substitute this expression for H into equation 1:

D + 7 = 3D - 17

Add 17 to both sides:

D + 24 = 3D

Subtract D from both sides:

24 = 2D

Divide by 2:

D = 12

So there are 12 candles on 's cake.