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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

Le the $$2$$ parts be $$x$$ and $$y$$
$$\therefore$$ According to question,

$$x+y= 24 ------ (i)$$
and $$7x+ 5y= 146 -------- (ii)$$

Multiplying eq $$(i)$$ by $$7$$, we get
$$7x+7y= 168 ----- (iii)$$
Subtracting eq. $$(ii)$$ by $$(iii)$$. we get

$$\quad 7x+7y=168\\ \quad 7x+5y=146\\ \quad -\quad \quad -\quad \quad \quad -\\ \quad ----------\\ \quad 2y=22\\ \quad ----------\\ \Rightarrow \quad y=11$$
But, $$x+y= 24 $$ (from eq. $$(i)$$)

$$x+11= 24 $$ (subtracting value of $$y$$ )

$$\Rightarrow x= 24-11 $$

$$\Rightarrow x=13$$

So, the $$2$$ parts are $$11$$ and $$13$$

Mathematics

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