Question

Raj, on his birthday, distributed chocolates in anorphanage. He gave 2 chocolates to eachchild and 20 chocolates to adults. Considering number of children as x and total number ofchocolates distributed is y, form the linear equation. If the total number of chocolatesdistributed is 150, how many children are there inthe orphanage. Explain the value depictedby Raj in the question.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{children}\mathrm{be}\mathrm{x}\mathrm{and}\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{chocolates}\mathrm{be}\mathrm{y}. \\ \mathrm{Since},\mathrm{Raj}\mathrm{distributed}150\mathrm{chocolates}\mathrm{so}\mathrm{y}=150.....\left(\mathrm{i}\right) \\ \mathrm{Also},\mathrm{Raj}\mathrm{gave}2\mathrm{chocolates}\mathrm{to}\mathrm{each}\mathrm{child}\mathrm{so}\mathrm{he}\mathrm{distributed}2\mathrm{x}\mathrm{chocolates}\mathrm{in}\mathrm{the}\mathrm{children}. \\ \mathrm{He}\mathrm{gave}20\mathrm{chocolates}\mathrm{to}\mathrm{adults}\mathrm{so}\mathrm{the}\mathrm{equation}\mathrm{becomes}2\mathrm{x}+20=\mathrm{y}.....\left(\mathrm{ii}\right) \\ \mathrm{Substituing}\left(\mathrm{i}\right)\mathrm{in}\left(\mathrm{ii}\right)\mathrm{we}\mathrm{get} \\ 2\mathrm{x}+20=150 \\ \Rightarrow 2\mathrm{x}=130 \\ \Rightarrow \mathrm{x}=65 \\ \mathrm{Thus},\mathrm{there}\mathrm{are}65\mathrm{children}\mathrm{in}\mathrm{the}\mathrm{orphanage}. \end{gathered}$$