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02 Jul 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
63% (03:14) correct
37%
(03:29)
wrong
based on 148
sessions
History
Date
Time
Result
Not Attempted Yet
Michael planned to spend $600 on renting workshop space for a specific number of hours at a certain hourly rate. However, he discovered that the rental rate was $20 higher per hour than he had anticipated. Consequently, he increased his budget to $800, but still ended up renting the space for 10 fewer hours than planned. What was the actual hourly rental rate for the workshop space?
A. 30
B. 35
C. 40
D. 50
E. 60
A. 30
B. 35
C. 40
D. 50
E. 60
03 Aug 2024, 02:45
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Bookmarks
Official Solution:
Michael planned to spend $600 on renting workshop space for a specific number of hours at a certain hourly rate. However, he discovered that the rental rate was $20 higher per hour than he had anticipated. Consequently, he increased his budget to $800, but still ended up renting the space for 10 fewer hours than planned. What was the actual hourly rental rate for the workshop space?
A. 30
B. 35
C. 40
D. 50
E. 60
Assume the actual hourly rental rate for the workshop space is \(p\) dollars. Then, at this rate, Michael would have rented the space for \(\frac{800}{p}\) hours.
The hourly rate at which Michael originally planned to rent the space would be \((p - 20)\) dollars, and at this rate, he planned to rent the space for \(\frac{600}{p-20}\) hours.
Given that the actual rental duration was 10 hours less than planned, we have:
\(\frac{800}{p} +10 = \frac{600}{p-20}\)
At this stage, plugging in the answer options to back-solve is easier.
By doing so, we find that option C fits: \(\frac{800}{40} +10 = 30\) and \( \frac{600}{p-20} = 30\).
Answer: C
Michael planned to spend $600 on renting workshop space for a specific number of hours at a certain hourly rate. However, he discovered that the rental rate was $20 higher per hour than he had anticipated. Consequently, he increased his budget to $800, but still ended up renting the space for 10 fewer hours than planned. What was the actual hourly rental rate for the workshop space?
A. 30
B. 35
C. 40
D. 50
E. 60
Assume the actual hourly rental rate for the workshop space is \(p\) dollars. Then, at this rate, Michael would have rented the space for \(\frac{800}{p}\) hours.
The hourly rate at which Michael originally planned to rent the space would be \((p - 20)\) dollars, and at this rate, he planned to rent the space for \(\frac{600}{p-20}\) hours.
Given that the actual rental duration was 10 hours less than planned, we have:
\(\frac{800}{p} +10 = \frac{600}{p-20}\)
By doing so, we find that option C fits: \(\frac{800}{40} +10 = 30\) and \( \frac{600}{p-20} = 30\).
Answer: C
General Discussion
02 Jul 2024, 03:05
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Actual Hourly rate - \(r\)
Actual rented hours - \(h\)
Actual scenario: \(h*r=800\)
Estimated scenario:
\((h+10)*(r-20)=600\)
\(hr-20h+10r-200=600\)
\(10r-20h=0\) (plugging in \(h*r=800\))
\(10r-\frac{20*800}{r}=0\) (plugging in \(h=\frac{800}{r}\))
\(10r^2-\frac{16000}{r}=0\)
\(r^2=1600\)
\(r=40\)
Answer is C.
Actual rented hours - \(h\)
Actual scenario: \(h*r=800\)
Estimated scenario:
\((h+10)*(r-20)=600\)
\(hr-20h+10r-200=600\)
\(10r-20h=0\) (plugging in \(h*r=800\))
\(10r-\frac{20*800}{r}=0\) (plugging in \(h=\frac{800}{r}\))
\(10r^2-\frac{16000}{r}=0\)
\(r^2=1600\)
\(r=40\)
Answer is C.
