Question

In a large hall there are 4x² rows of benches. If each row has 5x²y³ benches and each bench can accomodate xy² persons, determine the total number of persons if its is full up to its capacity.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{rows}\mathrm{in}\mathrm{the}\mathrm{hall}=4x^2, \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{benches}\mathrm{in}\mathrm{each}\mathrm{row}=5x^2{y}^3\mathrm{and} \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{persons}\mathrm{that}\mathrm{can}\mathrm{accomodate}\mathrm{in}\mathrm{a}\mathrm{bench}=x{y}^2 \\ \mathrm{Now},\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{benches}\mathrm{in}\mathrm{the}\mathrm{hall}=4x^2\times 5x^2{y}^3=20x^4{y}^3 \\ \mathrm{So},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{persons}\mathrm{in}\mathrm{the}\mathrm{hall}\mathrm{if}\mathrm{it}\mathrm{is}\mathrm{full}\mathrm{up}\mathrm{to}\mathrm{its}\mathrm{capacity}=x{y}^2\times 20x^4{y}^3=20x^5{y}^5 \end{gathered}$$