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

The value of b is 19.

Explanation:

With what the problem states, we have that:

`(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 = (10.64)/(0.56)`

`b = 19`

The value of b is 19.