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16 Sep 2014, 00:36
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If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A. \(2\)
B. \(5\)
C. \(\frac{100}{21}\)
D. \(\frac{110}{20}\)
E. \(\frac{9}{4}\)
A. \(2\)
B. \(5\)
C. \(\frac{100}{21}\)
D. \(\frac{110}{20}\)
E. \(\frac{9}{4}\)
10 Dec 2019, 10:33
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Here's a video explanation. Enjoy!
General Discussion
16 Sep 2014, 00:36
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Official Solution:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A. \(2\)
B. \(5\)
C. \(\frac{100}{21}\)
D. \(\frac{110}{20}\)
E. \(\frac{9}{4}\)
For a percentage questions like this one, it's almost always better to plug some smart numbers.
Let the usual price of a ticket be $20 (choose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was \(\frac{$4,400}{1.1}=$4,000;\)
Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was \(200*$21=$4,200\);
What percent less would last month's revenue be compared to this month's revenue: \(\text{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%\). General formula for percent increase or decrease, (percent change): \(\text{percent}=\frac{\text{Change}}{\text{Original}}*100\), so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.
Answer: C
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A. \(2\)
B. \(5\)
C. \(\frac{100}{21}\)
D. \(\frac{110}{20}\)
E. \(\frac{9}{4}\)
For a percentage questions like this one, it's almost always better to plug some smart numbers.
Let the usual price of a ticket be $20 (choose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was \(\frac{$4,400}{1.1}=$4,000;\)
Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was \(200*$21=$4,200\);
What percent less would last month's revenue be compared to this month's revenue: \(\text{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%\). General formula for percent increase or decrease, (percent change): \(\text{percent}=\frac{\text{Change}}{\text{Original}}*100\), so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.
Answer: C
