Question

derek is 70 and his granddaughter vanessa is 5. In how many years will vanessa by 1/6 derek's age?

Answer 1

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

Currently, Derek is 70 years old, and Vanessa is 5 years old. In \( x \) years, their ages will be:

- Derek's age: \( 70 + x \)
- Vanessa's age: \( 5 + x \)

We want to find \( x \) such that Vanessa's age will be \( \frac{1}{6} \) of Derek's age:

\[
5 + x = \frac{1}{6}(70 + x)
\]

Now, we'll eliminate the fraction by multiplying both sides by 6:

\[
6(5 + x) = 70 + x
\]

Distributing on the left side:

\[
30 + 6x = 70 + x
\]

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

\[
30 + 5x = 70
\]

Next, subtract 30 from both sides:

\[
5x = 40
\]

Now, divide by 5:

\[
x = 8
\]

Thus, in 8 years, Vanessa will be \( 5 + 8 = 13 \) years old, and Derek will be \( 70 + 8 = 78 \) years old. At that time, we can check:

\[
\frac{1}{6} \times 78 = 13
\]

This confirms that in 8 years, Vanessa will indeed be \( \frac{1}{6} \) of Derek's age. Therefore, the answer is:

\[
\boxed{8}
\]