Let the unknown quantity be represented by \( x \).
According to the problem, we have:
\[ x + \frac{3}{4}x + \frac{1}{3}x + \frac{1}{5}x = 89 \]
Now, we can combine these terms. To do this, we first need a common denominator for the fractions. The least common multiple (LCM) of \( 4, 3, \) and \( 5 \) is \( 60 \).
Now we can write each term with a denominator of \( 60 \):
\[ x = \frac{60}{60}x \]
\[ \frac{3}{4}x = \frac{3 \times 15}{4 \times 15}x = \frac{45}{60}x \]
\[ \frac{1}{3}x = \frac{1 \times 20}{3 \times 20}x = \frac{20}{60}x \]
\[ \frac{1}{5}x = \frac{1 \times 12}{5 \times 12}x = \frac{12}{60}x \]
Now we can combine these fractions:
\[ \frac{60}{60}x + \frac{45}{60}x + \frac{20}{60}x + \frac{12}{60}x = 89 \]
Adding the fractions gives us:
\[ \frac{60 + 45 + 20 + 12}{60}x = 89 \]
Calculating the numerator:
\[ 60 + 45 + 20 + 12 = 137 \]
So the equation simplifies to:
\[ \frac{137}{60}x = 89 \]
To isolate \( x \), multiply both sides by the reciprocal of \( \frac{137}{60} \):
\[ x = 89 \times \frac{60}{137} = \frac{5340}{137} \]
Thus, the quantity in fraction form is:
\[ \boxed{\frac{5340}{137}} \]