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Question

A person spent $$Rs 564$$ in buying pens and pencils if cost of each pen is $$Rs. 7$$ and each pencil is $$Rs. 3$$ and if the total number of things bought was $$108$$, how many of each type did he buy?


Solution

$$\Rightarrow$$  Let the number of pens be $$x.$$
$$\Rightarrow$$  Then, number of pencils $$=108-x$$
$$\Rightarrow$$  Cost of pens $$=7x$$
$$\Rightarrow$$  Cost of pencils $$=3(108-x)$$
According to the question,
$$7x+3(108-x)=564$$
$$7x+324-3x=564$$
$$4x+324=564$$
$$4x=564-324$$
$$4x=240$$
$$\therefore$$   $$x=\dfrac{240}{4}=60$$
$$\Rightarrow$$  Number of pencils $$=108-60=48$$
$$\therefore$$  The number of pens bought are $$60$$ and pencil bought are $$48$$. 

Maths

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