To solve Eric's riddle, we need to find a fraction that is equivalent to 25, and in which the numerator is 18 less than the denominator.
Let's denote the denominator of the fraction as \( d \). According to the riddle, the numerator \( n \) can be expressed as:
\[ n = d - 18 \]
The fraction is then:
\[ \frac{n}{d} = \frac{d - 18}{d} \]
We know that this fraction is equivalent to 25. This gives us the equation:
\[ \frac{d - 18}{d} = 25 \]
To eliminate the fraction, we multiply both sides by \( d \) (assuming \( d \neq 0 \)):
\[ d - 18 = 25d \]
Now, let's rearrange the equation to isolate \( d \):
\[ d - 25d = 18 \] \[ -24d = 18 \]
Now, divide both sides by -24:
\[ d = -\frac{18}{24} = -\frac{3}{4} \]
To find the numerator \( n \), substitute \( d \) back into the equation for \( n \):
\[ n = d - 18 \] \[ n = -\frac{3}{4} - 18 \]
To combine these, we can express 18 as a fraction over 4:
\[ n = -\frac{3}{4} - \frac{72}{4} = -\frac{75}{4} \]
So the fraction is:
\[ \frac{n}{d} = \frac{-\frac{75}{4}}{-\frac{3}{4}} = \frac{75}{3} \]
Now simplify \( \frac{75}{3} \):
\[ \frac{75}{3} = 25 \]
This verifies that \( \frac{n}{d} = 25 \) holds true. Thus, Eric's fraction is:
\[
- \frac{75}{4} / -\frac{3}{4} = 25. \]
So, the solution shows that Eric's fraction is equivalent to 25, and the terms fit the criteria specified in the riddle. The fraction itself is \( \frac{-75/4}{-3/4} \).
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