[Question]The cost of Joe's new HVAC system is $20,000. It includes 2 conditioning zones, each with 5 vents. In dollars, what is the cost of the system per vent?
[Answer]Two zones with 5 vents per zone is 2 * 5 = 10 vents. Thus, the $20,000 system costs $20,000 / 10 = $2,000 per vent. The answer is 2000.
Q: Tom's rabbit can run at 25 miles per hour. His cat can run 20 miles per hour. The cat gets a 15-minute head start. In hours, how long will it take for the rabbit to catch up?
A: The cat got a 15 / 60 = .25 hour head start. That means it ran 20 * .25 = 5 miles. The rabbit goes 25 - 20 = 5 mph faster than the cat. So it takes 5 / 5 = 1 hour for the rabbit to catch up. The answer is 1.
Question: Ali, Peter, and Joey were fishing. The fish Ali caught weighed, in sum, twice as much as the fish that Peter caught. Joey caught 1 kg more fish than Peter. Together the three of them caught 25 kg of fish. How many kilograms did Ali catch?
Answer: Let x be the weight of the fish that Peter caught. Then Ali and Joey caught 2 * x and x + 1 kg of fish, respectively. So, x + 2 * x + x + 1 = 25. So, 4 * x = 25 - 1 = 24. So, x = 6. Therefore, Ali caught 2 * x = 2 * 6 = 12 kg of fish. The answer is 12.
[Question]A truck driver has to spend $2 per gallon of gas. She can drive 10 miles per gallon. She drives at a rate of 30 miles per hour. If she is paid $.50 per mile, how much money does she make if she drives for 10 hours?
[Answer]The truck driver drives for 10 hours at 30 miles per hour, so she drives 10 * 30 = 300 miles. Therefore, she needs 300 / 10 = 30 gallons of gas. This will cost her 30 * $2 = $60. She will make 300 * $.50 = $150. Thus, after paying for gas, she will make $150 - $60 = $90. The answer is 90.
Q: James buys 200 lotto tickets for 2 dollars each. Of those tickets 20% are winners. 80% of the winners are for 5 dollars. 1 ticket is the grand prize of $5,000. The other tickets win an average of $10. How much did he profit?
A: He spent 200 * 2 = $400. There were 200 * .2 = 40 tickets. Of those 40 * .8 = 32 are 5 dollar winners. So they win 32 * 5 = $160. He has 40 - 32 = 8 other winning tickets. Of those 8 - 1 = 7 wins $10. So they win 10 * 7 = $70. So he won 5000 + 70 + 160 - 400 = $4830. The answer is 4830.
Question: Ray has 95 cents in nickels. If Ray gives 25 cents to Peter, and twice as many cents to Randi as he gave to Peter, how many nickels does Ray have left?
Answer:
Ray gave 25 * 2 = 50 cents to Randi. Ray has 95 - 25 - 50 = 20 cents in nickels left. Ray has 20 / 5 = 4 nickels. The answer is 4.