The sum of 35 and a certain number is divided by 4. The result is equals to double the number, find the number

Answer 1

Let the certain number be $x$.

According to the problem, we have the equation:

$$\frac{35+x}{4}=2x$$

To eliminate the fraction, we can multiply both sides by 4:

$$35+x=8x$$

Now, we can rearrange the equation by isolating $x$:

$$35=8x-x$$

$$35=7x$$

Next, we can solve for $x$ by dividing both sides by 7:

$$x=\frac{35}{7}=5$$

Thus, the certain number is $\boxed{{\displaystyle 5}}$.

To verify, we can substitute $x=5$ back into the original condition:

The sum of 35 and the number is:

$$35+5=40$$

Now dividing by 4 gives:

$$\frac{40}{4}=10$$

And double the number $x$ is:

$$2\times 5=10$$

Since both sides equal 10, our solution is confirmed. The certain number is indeed $\boxed{{\displaystyle 5}}$.