$\frac{1}{2}$ is subtracted from a number and the difference is multiplied by 4. If 25 is added to the product and the sum is divided by 3, the result is equal to 10. Find the number.

Given: $\frac{1}{2}$  is subtracted from a number and the difference is multiplied by 4. If 25 is added to the product and the sum is divided by 3, the result is equal to 10.

To find: Here we have to find the number.

Solution:

Let the number be  $=\ x$

Step 1: First, subtract $\frac{1}{2}$  from the number;

$x\ -\ \frac{1}{2}$

Step 2: Now, multiply it by 4;

$\left( x\ -\ \frac{1}{2}\right) \ \times \ 4\ =\ 4x\ -\ 2$

Step 3: Now, add 25 to it;

$4x\ -\ 2\ +\ 25\ =\ 4x\ +\ 23$

Step 4: Now, divide it by 3;

$\frac{4x\ +\ 23}{3}$

Step 5: Now, this is equal to 10;

$\frac{4x\ +\ 23}{3}\ =\ 10$

$4x\ +\ 23\ =\ 10\ \times\ 3$

$4x\ +\ 23\ =\ 30$

$4x\ =\ 30\ -\ 23$

$4x\ =\ 7$

$x\ =\ \frac{7}{4}$

So, the number is $\frac{7}{4}$.

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Updated on: 10-Oct-2022

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