On 's birthday, his brother Harry is seventeen years younger
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?
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.
To find out how many candles are on 's cake, we need to determine 's age. Let's start by defining some variables:
Let D be 's age.
Let H be Harry's age.
Therefore, we can set up the following equations based on the given information:
1. Harry is seventeen years younger than three times 's age: H = 3D - 17.
2. Tom is twelve years older than twice Harry's age: T = 2H + 12.
3. is seven years younger than his brother: D = H - 7.
We can solve this system of equations to find the ages of , Harry, and Tom.
First, substitute equation 3 into equation 1:
H = 3(H - 7) - 17.
Expand the equation:
H = 3H - 21 - 17.
Combine like terms:
H = 3H - 38.
Subtract 3H from both sides:
-2H = -38.
Divide both sides by -2:
H = 19.
Now that we know Harry's age is 19, we can substitute this value into equation 3 to find 's age:
D = H - 7 = 19 - 7 = 12.
Therefore, is 12 years old, and the number of candles on his cake would be 12.
Let's break down the information given step-by-step:
1. Let's assume 's age is "x" years.
2. According to the information, Harry is seventeen years younger than three times 's age, which can be represented as: Harry's age = 3x - 17.
3. Tom, the boys' father, is twelve years older than twice Harry's age. So, Tom's age = 2(3x - 17) + 12.
4. It's also given that is seven years younger than his brother Harry, so 's age = 3x - 17 - 7.
Now, let's simplify and solve for x:
5. 's age = 3x - 24.
Since it is 's birthday, the number of candles on his cake would correspond to his current age, which can be represented as x.
Therefore, the number of candles on 's cake would be x.