Bunuel wrote:
George can fill Q cans of paint in 3 minutes. If there are R cans of paint in one gallon, how many gallons can George fill in 45 minutes?
A. 30R/Q.
B. 15R/Q.
C. 30Q/R.
D. 5Q/R.
E. 15Q/R.
Another way: Choose numbers that are factors and/or multiples of 3 and 45. I set up proportion first to avoid inverting Q and R:
Q cans of paint in 3 minutes
\(\frac{Q cans}{3 mins}\) = \(\frac{X cans}{45 mins}\)
Let Q cans = 9
Let R, # of cans of paint in one gallon = 3
How many gallons do Q cans contain? 9 cans divided by 3 cans per gallon = 3 gallons.
Change the proportion units, where Q = 3
gallons:
\(\frac{3 gallons}{3 mins}\) = \(\frac{X gallons}{45 mins}\)
X = 45 gallons
Check answer choices with Q = 9, R = 3, looking for answer that yields
45A. 30R/Q = 90/9 = 10. NO
B. 15R/Q = 45/9 = 5. NO
C. 30Q/R = 270/3 = 90. NO
D. 5Q/R = 45/3 = 15. NO
E. 15Q/R = 135/3 = 45. YES
Answer E
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