Tickets to The Phantom of the Opera just lowered 15%. If the new price is $51.00, what was the original price?

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Answer 1 · 2017-05-15T20:45:09

Then $$ 51.00$ $$51.00$ is $100 % - 15 % = 85 %$ $100%-15%=85%$ of the original price.

Or:
$51 \div 85 = X \div 100 % \to$ $51div85=Xdiv100%->$

$85 \cdot X = 100 \cdot 51 \to X = \frac{100 \cdot 51}{85} = $ 60$ $85*X=100*51->X=(100*51)/85=$60$

Answer 2 · 2017-05-15T20:59:23

$$ 60$ $$60$

Here we have an example of reverse percentage. You know the amount AFTER a change has happened, but we do not know the starting amount.

The starting amount represents $100 %$ $100%$ and the changed amount of $$ 51$ $$51$ represents $85 % from 100 % - 15 %$ $85% " from " 100%-15%$

You can use direct proportion because we are comparing percents and amounts.

$\frac{x}{100} = \frac{51}{85} \frac{\leftarrow amount in dollars}{\leftarrow percent}$ $x/100 = 51/85" "(larr"amount in dollars")/(larr"percent")$

$85 x = 51 \times 100$ $85x = 51 xx100" "$ by cross-multiplying

$x = \frac{51 \times 100}{85}$ $x = (51xx100)/85$

$x = $ 60$ $x = $60$

You could also have written the proportion in this form to get the same result:

$\frac{51}{x} = \frac{85}{100}$ $51/x = 85/100$