Question

enrique is 61 and his niece zoe is 7. In how many years will zoe be 1/4 enrique's age?

Answer 1

To find out in how many years Zoe will be 1/4 of Enrique's age, let's define the number of years from now as \( x \).

Currently, Enrique is 61 and Zoe is 7. In \( x \) years, their ages will be:

- Enrique's age will be \( 61 + x \)
- Zoe's age will be \( 7 + x \)

We set up the equation for when Zoe's age will be 1/4 of Enrique's age:

\[
7 + x = \frac{1}{4}(61 + x)
\]

Now, we will multiply both sides by 4 to eliminate the fraction:

\[
4(7 + x) = 61 + x
\]

Distributing the 4 on the left side:

\[
28 + 4x = 61 + x
\]

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

\[
28 + 4x - x = 61
\]

This simplifies to:

\[
28 + 3x = 61
\]

Next, we subtract 28 from both sides:

\[
3x = 61 - 28
\]

Calculating the right side:

\[
3x = 33
\]

Now, divide both sides by 3:

\[
x = 11
\]

Thus, in 11 years, Zoe will be \( 7 + 11 = 18 \) and Enrique will be \( 61 + 11 = 72 \).

To verify, we check:

\[
\frac{1}{4}(72) = 18
\]

So, indeed, in 11 years, Zoe will be 1/4 of Enrique's age.

The answer is \( \boxed{11} \).