Ten years ago, Heather was twice as old as her brother David. Today, she is 12 years older than him. How old are they both today?
Heather's age today: 27
David's age today: 15
Thanks in advance! I tried using other solutions from Google and just am not sure I got it right.
To solve this problem, let's break it down step by step.
Step 1: Define the variables
Let's assume that Heather's current age is H, and David's current age is D.
Step 2: Translate the given information into equations
According to the problem, ten years ago, Heather was twice as old as her brother David. This can be expressed as:
(H - 10) = 2(D - 10) -- (Equation 1)
Additionally, it is stated that today Heather is 12 years older than David, which can be expressed as:
H = D + 12 -- (Equation 2)
Step 3: Solve the equations
Now, we have a system of two equations with two variables. We can solve this system to find the values of H and D.
From Equation 2, we can substitute the value of H into Equation 1:
(D + 12 - 10) = 2(D - 10)
Simplifying, we have:
D + 2 = 2D - 20
Rearranging terms, we get:
D - 2D = -20 - 2
Simplifying further, we have:
-D = -22
Multiplying both sides by -1, we get:
D = 22
Now we can substitute the value of D into Equation 2 to find H:
H = 22 + 12
H = 34
Step 4: Answer the question
Therefore, Heather is currently 34 years old (H = 34) and David is 22 years old (D = 22).
Hence, the answer is:
Heather's age today: 34
David's age today: 22