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

Hint:Here, let the first number be x, then the second number will be (24 – x). Also form mathematical equations using the second condition given in question. Solve the equation and find the value of x. Value of x obtained will be the first number and (24 – x) will be the second number.

Complete step by step answer:
Let the first part be x and second part be (24 – x). Now according to given condition,
$7x + 5(24 – x) = 146$
On simplifying
$7x + 120 – 5x = 146$
On separating constants and variables
$2x = 146 – 120\\
\Rightarrow 2x = 26\\
\Rightarrow x = 13$

Therefore, the first number is 13 and the second number is (24 – x) = 24 – 13 = 11.

Verification:
Condition 1: Sum of two numbers should be $24$.
$13 + 11 = 24$ (Satisfied)
Condition 2: 7 times the first part added to 5 times the second part makes $146$.
7 times the first number means $7 \times 13 = 91$.
And 5 times of second numbers means $5 \times 11 = 55$.
$91 + 55 = 146$ (Satisfied)

Note: In these types of questions, form mathematical equations based on conditions given in question by letting variable value like x. By solving the equation and finding the numbers. Also check whether the value obtained satisfies the given conditions or not. Do not let two numbers as x and y and make two equations containing x and y as variables, as this will make the solution complicated. In this question we can simply let x and (24 – x).