Alice notices that doubling her age and then adding 3 is the same as subtracting 7 from her age and then multiplying it by 3. How old is Alice?

Question

15
32
20
24

Answer 1

Let Alice's age be \( x \).

According to the problem, we have the following equation:

\[ 2x + 3 = 3(x - 7) \]

Now, let's solve for \( x \).

First, distribute the 3 on the right side:

\[ 2x + 3 = 3x - 21 \]

Next, we can rearrange the equation by subtracting \( 2x \) from both sides:

\[ 3 = x - 21 \]

Now, add 21 to both sides:

\[ x = 24 \]

Thus, Alice's age is \( \boxed{24} \).