Question

The age distribution of people entering a Museum X is shown in the pie graph above. Visitors aged $0-9$ years get into Museum for free, visitors aged $50$ and older pay 5$foradmissionandeveryoneelsepays$ $10$. If number of people that are above $20$ years and entering the museum are $553$, the find the revenue generated by the museum from tickets sold to people aged $40$ and older in 2014?

Answer 1

Let the total number of people be $N$.

Then the number of people having an age of $20$ years or above is

$0.19N+0.27N+0.25N+0.08N=553$

$\Rightarrow 0.79N=553$

$\Rightarrow N=700$

Hence, the total number of people entering the museum on that day is $700$.

Now the gross revenue is

$700\left[\right(0.05)\times 0+(0.08)\times 5+(0.87)\times 10)]$

$=700[0.4+8.7]$

$=700\left(9.1\right)=6370$

The revenue generated from selling tickets to people having an age of $40$ or above is

$=700\left[\right(0.25)\times 10+(0.08)\times 5]=2030$