[Question]A quarterback throws 50 passes in one game. He throws twice as many passes to the right of the field than he does to the left of the field. He throws 2 more passes to the center of the field than he did to the left. How many passes did he throw to the left side of the field?
[Answer]Let x represent the number of passes thrown to the left side of the field. Right:2x. Center:x + 2. Total:x + 2x + x + 2 = 50. 4x + 2 = 50. 4x = 48. x = 12 passes. The answer is 12.
Q: Anthony keeps a bottle of vinegar in his cupboard for 2 years. Each year 20% of the vinegar evaporates. What percent of the vinegar is left after 2 years?
A: First find what percent of the vinegar is still in the bottle after each year: 100% - 20% = 80%. Then multiply the amount of vinegar left after one year by the percentage left after each year to find how much is left after 2 years: 80% * 80% = 64%. The answer is 64.
Question: A tank contains 6000 liters of water, 2000 liters evaporated, and then 3500 liters were drained by Bob. How many liters are in the tank if it now rains for 30 minutes and every 10 minutes 350 liters of rain are added to the tank?
Answer: After the first evaporation, the water tank has 6000 liters - 2000 liters = 4000 liters. After the second extraction, the water tank has 4000 liters - 3500 liters = 500 liters. The tank is refilled with rain 30 minutes / 10 minutes = 3 times. The amount of water refilled with rain is 3 times * 350 liters per time = 1050 liters. With the additional rainwater, the water tank has 500 liters + 1050 liters = 1550 liters. The answer is 1550.
[Question]Emma and Briana invested some capital into a business. Emma's investment is supposed to yield 15% of the capital annually while Briana's should yield 10% annually. If Emma invested $300 and Briana invested $500, what will be the difference between their return-on-investment after 2 years?
[Answer]15% of $300 is (15 / 100) * $300 = $45. Emma will earn an annual ROI of $45 for 2 years for a total of $45 * 2 = $90. 10% of $500 is (10 / 100) * $500 = $50. Briana will earn an annual ROI of $50 for 2 years for a total of $50 * 2 = $100. The difference between their ROI after 2 years is $100 - $90 = $10. The answer is 10.
Q: Samuel is driving to San Francisco’s Comic-Con in his car and he needs to travel 600 miles to the hotel where he made a reservation. At first, he drives at 50 miles/hour for 3 hours straight, then he speeds up to 80 miles/hour for 4 hours. How far is he from the hotel?
A: At first at 50 miles / hour he travels 50 miles / hours * 3 hours = 150 miles. After that, he speeds up, traveling 80 miles / hours * 4 hours = 320 miles. He travels a total of 150 miles + 320 miles = 470 miles. He is 600–470 = 130miles from the hotel. The answer is 130.
Question: The lifespan of a hamster is 6 years less than that of a bat. The lifespan of a frog is 4 times that of a hamster. Altogether, the lifespan of the animals is 30 years. What is the lifespan of the bat?
Answer:
Let’s set up an equation by calling the lifespan of a bat x, and therefore the lifespan of the hamster x – 6, and the lifespan of the frog 4 (x – 6) which add together to equal 30, like this: x + x – 6 + 4 (x – 6) = 30. That gives us 6x – 30 = 30 and we should add 30 to each side to try to isolate the x. Now we have 6x = 60, which we will divide by 6, 6x / 6 = 60 / 6. This gives us x = 10. The bat has a lifespan of 10 years. The answer is 10.
[Question]A quarterback throws 50 passes in one game. He throws twice as many passes to the right of the field than he does to the left of the field. He throws 2 more passes to the center of the field than he did to the left. How many passes did he throw to the left side of the field?
[Answer]Let x represent the number of passes thrown to the left side of the field. Right:2x. Center:x + 2. Total:x + 2x + x + 2 = 50. 4x + 2 = 50. 4x = 48. x = 12 passes. The answer is 12.
Q: Anthony keeps a bottle of vinegar in his cupboard for 2 years. Each year 20% of the vinegar evaporates. What percent of the vinegar is left after 2 years?
A: First find what percent of the vinegar is still in the bottle after each year: 100% - 20% = 80%. Then multiply the amount of vinegar left after one year by the percentage left after each year to find how much is left after 2 years: 80% * 80% = 64%. The answer is 64.
Question: A tank contains 6000 liters of water, 2000 liters evaporated, and then 3500 liters were drained by Bob. How many liters are in the tank if it now rains for 30 minutes and every 10 minutes 350 liters of rain are added to the tank?
Answer: After the first evaporation, the water tank has 6000 liters - 2000 liters = 4000 liters. After the second extraction, the water tank has 4000 liters - 3500 liters = 500 liters. The tank is refilled with rain 30 minutes / 10 minutes = 3 times. The amount of water refilled with rain is 3 times * 350 liters per time = 1050 liters. With the additional rainwater, the water tank has 500 liters + 1050 liters = 1550 liters. The answer is 1550.
[Question]Emma and Briana invested some capital into a business. Emma's investment is supposed to yield 15% of the capital annually while Briana's should yield 10% annually. If Emma invested $300 and Briana invested $500, what will be the difference between their return-on-investment after 2 years?
[Answer]15% of $300 is (15 / 100) * $300 = $45. Emma will earn an annual ROI of $45 for 2 years for a total of $45 * 2 = $90. 10% of $500 is (10 / 100) * $500 = $50. Briana will earn an annual ROI of $50 for 2 years for a total of $50 * 2 = $100. The difference between their ROI after 2 years is $100 - $90 = $10. The answer is 10.
Q: Samuel is driving to San Francisco’s Comic-Con in his car and he needs to travel 600 miles to the hotel where he made a reservation. At first, he drives at 50 miles/hour for 3 hours straight, then he speeds up to 80 miles/hour for 4 hours. How far is he from the hotel?
A: At first at 50 miles / hour he travels 50 miles / hours * 3 hours = 150 miles. After that, he speeds up, traveling 80 miles / hours * 4 hours = 320 miles. He travels a total of 150 miles + 320 miles = 470 miles. He is 600–470 = 130miles from the hotel. The answer is 130.
Question: The lifespan of a hamster is 6 years less than that of a bat. The lifespan of a frog is 4 times that of a hamster. Altogether, the lifespan of the animals is 30 years. What is the lifespan of the bat?
Answer:
user
Let’s set up an equation by calling the lifespan of a bat x, and therefore the lifespan of the hamster x – 6, and the lifespan of the frog 4 (x – 6) which add together to equal 30, like this: x + x – 6 + 4 (x – 6) = 30. That gives us 6x – 30 = 30 and we should add 30 to each side to try to isolate the x. Now we have 6x = 60, which we will divide by 6, 6x / 6 = 60 / 6. This gives us x = 10. The bat has a lifespan of 10 years. The answer is 10.
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[Question]A quarterback throws 50 passes in one game. He throws twice as many passes to the right of the field than he does to the left of the field. He throws 2 more passes to the center of the field than he did to the left. How many passes did he throw to the left side of the field?
[Answer]Let x represent the number of passes thrown to the left side of the field. Right:2x. Center:x + 2. Total:x + 2x + x + 2 = 50. 4x + 2 = 50. 4x = 48. x = 12 passes. The answer is 12.
Q: Anthony keeps a bottle of vinegar in his cupboard for 2 years. Each year 20% of the vinegar evaporates. What percent of the vinegar is left after 2 years?
A: First find what percent of the vinegar is still in the bottle after each year: 100% - 20% = 80%. Then multiply the amount of vinegar left after one year by the percentage left after each year to find how much is left after 2 years: 80% * 80% = 64%. The answer is 64.
Question: A tank contains 6000 liters of water, 2000 liters evaporated, and then 3500 liters were drained by Bob. How many liters are in the tank if it now rains for 30 minutes and every 10 minutes 350 liters of rain are added to the tank?
Answer: After the first evaporation, the water tank has 6000 liters - 2000 liters = 4000 liters. After the second extraction, the water tank has 4000 liters - 3500 liters = 500 liters. The tank is refilled with rain 30 minutes / 10 minutes = 3 times. The amount of water refilled with rain is 3 times * 350 liters per time = 1050 liters. With the additional rainwater, the water tank has 500 liters + 1050 liters = 1550 liters. The answer is 1550.
[Question]Emma and Briana invested some capital into a business. Emma's investment is supposed to yield 15% of the capital annually while Briana's should yield 10% annually. If Emma invested $300 and Briana invested $500, what will be the difference between their return-on-investment after 2 years?
[Answer]15% of $300 is (15 / 100) * $300 = $45. Emma will earn an annual ROI of $45 for 2 years for a total of $45 * 2 = $90. 10% of $500 is (10 / 100) * $500 = $50. Briana will earn an annual ROI of $50 for 2 years for a total of $50 * 2 = $100. The difference between their ROI after 2 years is $100 - $90 = $10. The answer is 10.
Q: Samuel is driving to San Francisco’s Comic-Con in his car and he needs to travel 600 miles to the hotel where he made a reservation. At first, he drives at 50 miles/hour for 3 hours straight, then he speeds up to 80 miles/hour for 4 hours. How far is he from the hotel?
A: At first at 50 miles / hour he travels 50 miles / hours * 3 hours = 150 miles. After that, he speeds up, traveling 80 miles / hours * 4 hours = 320 miles. He travels a total of 150 miles + 320 miles = 470 miles. He is 600–470 = 130miles from the hotel. The answer is 130.
Question: The lifespan of a hamster is 6 years less than that of a bat. The lifespan of a frog is 4 times that of a hamster. Altogether, the lifespan of the animals is 30 years. What is the lifespan of the bat?
Answer:
Let’s set up an equation by calling the lifespan of a bat x, and therefore the lifespan of the hamster x – 6, and the lifespan of the frog 4 (x – 6) which add together to equal 30, like this: x + x – 6 + 4 (x – 6) = 30. That gives us 6x – 30 = 30 and we should add 30 to each side to try to isolate the x. Now we have 6x = 60, which we will divide by 6, 6x / 6 = 60 / 6. This gives us x = 10. The bat has a lifespan of 10 years. The answer is 10.