Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146.
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.
Solution:
Let one part be $\mathrm{x}$.
7 times the first part $=7 \mathrm{x}$
Let the other part be $(24-\mathrm{x})$.
5 times the second part $=5(24-\mathrm{x})$
$\therefore 7 x+5(24-x)=146$
$\Rightarrow 7 x+120-5 x=146$
$\Rightarrow 7 x-5 x=146-120$
$\Rightarrow 2 x=26$
$\Rightarrow x=\frac{26}{2}=13$
Therefore, one part is 13 .
Other part $=(24-x)=(24-13)=11$
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