Question

Twenty four is divided into two parts such that $7$ times the first part added to $5$ times the second part makes $146$. Find each part.

Answer 1

Step 1: Let's find the value of $x$

Let us assume the first part as $x$ and second part be $\left(24-x\right)$

Now, as per the given condition,

$7x+5(24-x)=146$

On further calculation, we get,

$\begin{array}{rcl}7x+120-5x& =& 146\\ 2x+120& =& 146\\ 2x& =& 146-120\\ 2x& =& 26\\ x& =& \frac{26}{2}\\ x& =& 13\\ & & \end{array}$

Now, $\left(24-x\right)=(24-13)=11$

Step 2: Verification with conditions.

Condition $1$:

Sum of two numbers $=24$

$13+11=24$ (Satisfied)

Condition $2$:

$7$ times the first part added to 5 times the second part makes $146$

$7$ times the first number $7\times 13=91$

$5$ times the second part $=5\times 11=55$

$91+55=146$ (Satisfied)

Hence the first numbers is $13$ and the second number is $11$.