Question

solve the problem algebraically. clearly define all variables, write an appropriate equation, and solve.

when the same number is added to the numerator and denominator of the fraction \\(\frac{3}{5}\\), the result is \\(\frac{17}{24}\\). what is that number?

the number is
(type an integer or a simplified fraction.)

Explanation:

Define the variable and set up the equation

Let \(x\) be the number added to both the numerator and the denominator.

$$ \frac{3 + x}{5 + x} = \frac{17}{24} $$

Solve the equation using cross-multiplication

$$
LATEXBLOCK0
$$

Answer:

When the same number is added to the numerator and denominator of the fraction \(\frac{3}{5}\), the result is \(\frac{17}{24}\). What is that number?

The number is <blank>\(\frac{13}{7}\)</blank>