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 \( \boxed{11} \).
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