Question

The decimal $0.76$ is equal to the fraction $\frac{4b+19}{6b+11}$, where $b$ is a positive integer. What is the value of $b$?

Answer 1

Answer:

The value of b is 19.

Step-by-step explanation:

With what the problem states, we have that:

$\frac{4b + 19}{6b + 11} = 0.76$

Doing cross multiplication

$4b + 19 = 0.76(6b + 11)$

$4b + 19 = 4.56b + 8.36$

$4.56b - 4n = 19 - 8.36$

$0.56b = 10.64$

$b = \frac{10.64}{0.56}$

$b = 19$

The value of b is 19.