Question

There are a few families residing in a localty.For a festival some families donated Rs 100 each the other families donated Rs 50 each.The total money collected was Rs 44,450.Express this in the form of an equation in two variables.Using this equation , find the no. of families who donated Rs 100 each if the no. of families donating Rs 50 is 111

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{families}\mathrm{who}\mathrm{donated}\mathrm{Rs}100=x \\ \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{families}\mathrm{who}\mathrm{donated}\mathrm{Rs}50=y \\ \mathrm{Now},\mathrm{total}\mathrm{donation}=\mathrm{Rs}44,450 \\ So,100x+50y=44450 \\ \mathrm{The}\mathrm{above}\mathrm{is}\mathrm{the}\mathrm{required}\mathrm{linear}\mathrm{equation}. \\ \mathrm{Now},\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that},\mathrm{number}\mathrm{of}\mathrm{families}\mathrm{who}\mathrm{donated}\mathrm{Rs}50\mathrm{is}111. \\ \mathrm{Put}y=111\mathrm{in}\mathrm{the}\mathrm{above}\mathrm{equation},\mathrm{we}\mathrm{get} \\ 100x+50\times 111=44450 \\ \Rightarrow 100x+5550=44450 \\ \Rightarrow 100x=38900 \\ \Rightarrow x=389 \\ \mathrm{So},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{families}\mathrm{who}\mathrm{donated}\mathrm{Rs}100=389 \end{gathered}$$