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Price of the ticket at amusement park was cut down. In the result there was 50% more visitors in the park. At the same time profit from tickets' sale raised by 20%.

What was the rebate for the ticket(how much ticket's price went down)?

My solution:

variables:

x - ticket' price

y - number of people who have visited the park before price cut

z - price cut(rebate)

Equasion: $$ (1-z)x \cdot 1,5y=1,2xy $$

$$ z = 0.2 $$

Thus ticket price wen down by 20%.

Question: Am I right? It seems bit too easy.

Yoda
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  • Looks good to me. $1.5p_{new}=1.2p_{old}$ so $p_{new}=0.8p_{old}$ a reduction of $20$ percent – drhab Apr 08 '14 at 16:57

1 Answers1

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What you know is that $$ \text{The new income} = 120\%\text{ of the old income} $$ The new income is price per ticket, which is $(1-z)x$, times the number of tickets sold, $1.5y$. So your left hand side is good.

The old revenue was the old price of tickets, $x$, times the old number of guests, $y$. Multiply by $1.2$ to get the increase of $20\%$. All in all you get $$ (1-z)x\cdot 1.5y = 1.2xy $$ which is exactly your equation.

If it seems easy it's only because you found the elegant way of solving it and / or this is an elegantly posed problem. Finding solutions like this is part of the joy of mathematics for many people, including me.

Arthur
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