Let's denote Morolake's current age as \( x \).
Nine years ago, Morolake's age was \( x - 9 \). According to the problem, \( \frac{1}{4} \) of her age nine years ago is equal to \( \frac{1}{5} \) of her age next year. Next year, Morolake's age will be \( x + 1 \).
Setting up the equation based on the information given:
\[ \frac{1}{4}(x - 9) = \frac{1}{5}(x + 1) \]
Now we can eliminate the fractions by multiplying both sides by 20 (the least common multiple of 4 and 5):
\[ 20 \cdot \frac{1}{4}(x - 9) = 20 \cdot \frac{1}{5}(x + 1) \]
This simplifies to:
\[ 5(x - 9) = 4(x + 1) \]
Expanding both sides:
\[ 5x - 45 = 4x + 4 \]
Now, subtract \( 4x \) from both sides:
\[ 5x - 4x - 45 = 4 \] \[ x - 45 = 4 \]
Next, add 45 to both sides:
\[ x = 49 \]
Thus, Morolake is currently \( \boxed{49} \) years old.
To verify:
- Nine years ago, Morolake was \( 49 - 9 = 40 \).
- Next year, her age will be \( 49 + 1 = 50 \).
Calculating the values:
- \( \frac{1}{4} \) of 40 is \( 10 \).
- \( \frac{1}{5} \) of 50 is \( 10 \).
Both sides are equal, confirming the solution is correct. Morolake is indeed \( \boxed{49} \) years old.
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