Question

​In a mathematics quiz, 30 prizes consisting 1st and 2nd only are to be given. 1st and 2nd prizes are worth ' 2000 and ' 1000, respectively. If the total prize money is ' 52,000 then show that:
(a) If 1st prizes are x in number then the numbers of 2nd prizes are
(b) The total value of prizes in terms of x are
(c) The equation formed is
(d) The solution of the equation is
(e) The number of 1st prizes are
(f) The number of 2nd prizes are

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right). \\ \mathrm{Number}\mathrm{of}\mathrm{first}\mathrm{prizes}=\mathrm{x} \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{prizes}=30 \\ \mathrm{So}\mathrm{number}\mathrm{of}\mathrm{second}\mathrm{prizes}=30-\mathrm{x} \\ \left(\mathrm{b}\right). \\ \mathrm{Number}\mathrm{of}\mathrm{first}\mathrm{prizes}=\mathrm{x} \\ \mathrm{Value}\mathrm{of}\mathrm{each}\mathrm{first}\mathrm{prize}=\mathrm{Rs}2000 \\ \mathrm{Number}\mathrm{of}\mathrm{second}\mathrm{prizes}=30-\mathrm{x} \\ \mathrm{Value}\mathrm{of}\mathrm{each}\mathrm{second}\mathrm{prize}=\mathrm{Rs}1000 \\ \mathrm{Total}\mathrm{value}\mathrm{of}\mathrm{prizes}=2000\mathrm{x}+1000\left(30-\mathrm{x}\right)=2000\mathrm{x}+30000-1000\mathrm{x}=\mathrm{Rs}\left(1000\mathrm{x}+30000\right) \\ \left(\mathrm{c}\right). \\ \mathrm{The}\mathrm{equation}\mathrm{formed}\mathrm{is}, \\ 1000\mathrm{x}+30000=52000 \\ \left(\mathrm{d}\right). \\ 1000\mathrm{x}+30000=52000 \\ \Rightarrow 1000\mathrm{x}=52000-30000 \\ \Rightarrow 1000\mathrm{x}=22000 \\ \Rightarrow \mathrm{x}=22 \\ \left(\mathrm{e}\right). \\ \mathrm{Number}\mathrm{of}\mathrm{first}\mathrm{prizes}=\mathrm{x}=22 \\ \left(\mathrm{f}\right). \\ \mathrm{Number}\mathrm{of}\mathrm{second}\mathrm{prizes}=30-\mathrm{x}=30-22=8 \end{gathered}$$