Question

todd is 33 years old; his nephew jacob is 12. in how many years will jacob be half his uncle todd's age?

Answer 1

Let's denote the number of years from now as \( x \).

In \( x \) years, Todd's age will be \( 33 + x \) and Jacob's age will be \( 12 + x \).

We want to find when Jacob's age will be half of Todd's age:

\[
12 + x = \frac{1}{2}(33 + x)
\]

To eliminate the fraction, we can multiply both sides of the equation by 2:

\[
2(12 + x) = 33 + x
\]

This simplifies to:

\[
24 + 2x = 33 + x
\]

Next, we can subtract \( x \) from both sides:

\[
24 + x = 33
\]

Now, subtract 24 from both sides:

\[
x = 33 - 24
\]

\[
x = 9
\]

In 9 years, Jacob will be half of Todd's age. To verify:

- In 9 years, Todd will be \( 33 + 9 = 42 \).
- In 9 years, Jacob will be \( 12 + 9 = 21 \).

Indeed, \( 21 \) is half of \( 42 \).

Thus, the answer is that in **9 years** Jacob will be half his uncle Todd's age.