M39-77

Question

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

Show Answer

Official Answer

C

A. 30
B. 35
C. 40
D. 50
E. 60

Bunuel · Answer

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

Show Answer

Official Answer

C

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

totamofficiis · Answer

I like the solution - it’s helpful.

gt2379 · Answer

Why doesn't this equation work:

-   = 10

I'm getting x = 20, but the answer is 40. Can you help explain why the above equation doesn't work?

Bunuel · Answer

Your equation is fine if x is the planned rate, so x = 20 means the actual rate is x + 20 = 40.

gt2379 · Answer

Thank you makes sense now

Vivek1707 · Answer

This is a great question that’s helpful for learning.

officiisnobis · Answer

I like the solution - it’s helpful. i solved for planned rate by mistake

Sneha_0410 · Answer

Let H → hour planned
And R → hourly rate planned

600 = HR
800 = ( H -10 ) ( R+ 20 )

After solving... We get
H = 30
R = 20

We need to find the actual hour → 20+20 = 40

nobisex · Answer

I like the solution - it’s helpful. I think backsolving using answer options would be beneficial here.

A possible way could be quickly eliminating options A,B and E since they result in non integer values for the number of actual hours.

Options C and D could be then be tested to verify the correct answer.

M39-77

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