judy is now twice as old as adam, but six years ago, she was 5 times as old as he was. how old is judy now?

Answer 1

Let's denote Judy's current age as \( J \) and Adam's current age as \( A \).

From the problem, we have two pieces of information:

1. Judy is now twice as old as Adam: \[ J = 2A \]

2. Six years ago, Judy was 5 times as old as Adam: \[ J - 6 = 5(A - 6) \]

Now, let's solve these equations step-by-step.

First, substitute the expression for \( J \) from the first equation into the second equation:

\[ 2A - 6 = 5(A - 6) \]

Now, expand the right side:

\[ 2A - 6 = 5A - 30 \]

Next, rearranging the equation gives:

\[ 2A - 5A = -30 + 6 \] \[ -3A = -24 \] \[ A = 8 \]

Now that we know Adam's age, we can find Judy's age using the first equation:

\[ J = 2A = 2 \times 8 = 16 \]

Thus, Judy is currently 16 years old.

To verify our solution, let's check the second condition:

• Six years ago, Judy's age was \( 16 - 6 = 10 \) and Adam's age was \( 8 - 6 = 2 \).
• Indeed, six years ago, Judy was \( 10 \) years old, which is \( 5 \times 2 \) (Adam's age at that time).

Everything checks out, confirming that Judy is 16 years old now.