Question

To a certain number $6$ is added. The sum is multiplied by $6$ and the product is divided by $13$, then $7$ is subtracted from the quotient. If the number obtained after these operations is $5$, then the original number is

Answer 1

Let the starting number be $x$.

Let's write each step separately.

In the first step, we add 6. So, the result is $x+6$.

In the second step, we multiply the result by 6 to get $6x+36$.

In the third step, we divide the result by 13 to get $\frac{6x+36}{13}.$

In the last step, we subtract 7 from the result to get $=\frac{6x+36}{13}-7=\frac{6x-55}{13}$.

It is given to us that this number is equal to 5.

Therefore, to find $x$,

we solve the following equation :

$\frac{6x-55}{13}=5$.

$⟹6x-55=65$

$⟹6x=120$

$⟹x=20$.