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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