Question

walter is 43 years old; his daughter Paulette is 7. In how many years will Paulette be one-third of walter's age?

Answer 1

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

In \(x\) years, Walter's age will be \(43 + x\) and Paulette's age will be \(7 + x\). We want to find \(x\) such that Paulette's age will be one-third of Walter's age:

\[
7 + x = \frac{1}{3}(43 + x)
\]

To eliminate the fraction, we can multiply both sides by 3:

\[
3(7 + x) = 43 + x
\]

Expanding both sides gives:

\[
21 + 3x = 43 + x
\]

Now, we can isolate \(x\) by subtracting \(x\) from both sides:

\[
21 + 2x = 43
\]

Next, we subtract 21 from both sides:

\[
2x = 22
\]

Now, divide both sides by 2:

\[
x = 11
\]

So, in 11 years, Paulette will be one-third of Walter's age.

Now let's verify:
In 11 years, Walter will be:

\[
43 + 11 = 54
\]

And Paulette will be:

\[
7 + 11 = 18
\]

Now checking if Paulette's age is one-third of Walter's age:

\[
\frac{54}{3} = 18
\]

This confirms that in 11 years, Paulette will indeed be one-third of Walter's age.

Thus, the answer is \( \boxed{11} \).