Question

A person spent Rs.564 in buying pens and pencils. If the 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?

Answer 1

Hint – To find the number of each type he bought, we consider the number of pens to be a variable x, expressing the number of pencils in terms of x. Then we find their costs and establish an equation with the given. Then we solve the equation for the answer.
Complete step by step answer:
Let the number of pens be x
Therefore the number of pencils = Total – number of pens = 108 – x
Now cost of x pens = Cost per pen × number of pens = 7x
Similarly cost of pencils = cost per pencil × number of pencils = 3(108 – x)

Given total amount spent = Rs.564
Total amount = cost of total pens + cost of total pencils
⟹7x + 3(108 – x) = 564
⟹7x – 3x + 324 = 564
⟹4x = 240
⟹x = $\dfrac{{240}}{4} = 60$
Therefore 108 –x = 108 – 60 = 48.
Hence, the number of pens are 60 and the number of pencils are 48.

Note – In order to solve questions of this type the key is to understand the relationship between all the given terms and the unknown to be determined. A good observation of the question is appreciated as every single sentence in the questions helps us build the relationship.