Question

The numerator of a rational number is 3 less than five times its denominator. When 2 is subtracted from its numerator, and 7 is added to its denominator, the simplest form of the rational number obtained is 5/3. Find the original rational number.

A. 5/8
B. 2/3
C. 7/4
D. 3/5

Answer 1

To solve the problem, we assumed the original denominator as x and followed the given conditions to create an equation. Solving this equation, we found the denominator to be 5, yielding the original rational number as 22/5. This solution doesn't match with any of the provided answer choices, suggesting an error in the provided options.

Step-by-step explanation:

The question is to find the original rational number given that its numerator is 3 less than five times its denominator. Let's assume the denominator is x and thus the numerator will be 5x - 3. The modified fraction after subtracting 2 from the numerator and adding 7 to the denominator becomes 5/3. So, we have:

(5x - 3 - 2) / (x + 7) = 5/3

Simplifying the numerator gives us (5x - 5) / (x + 7) = 5/3. By cross multiplication, we get:

3(5x - 5) = 5(x + 7)

15x - 15 = 5x + 35

15x - 5x = 35 + 15

10x = 50

x = 5

Now, having the denominator, we can find the original numerator:

5x - 3 = 5(5) - 3 = 25 - 3 = 22

Thus, the original rational number is 22/5, which is not listed in the answer choices, indicating a potential error in the choices provided.