Question: 4/5 of the Easter eggs are blue and 1/5 are purple. Half the purple eggs have five pieces of candy each, and 1/4 of the blue eggs do. The rest of the eggs only have one piece of candy. If Jerry opens one egg at random, what is the percentage chance he'll get 5 pieces of candy?
Answer: First find the probability Jerry gets a blue egg with 5 pieces of candy by multiplying the independent probabilities: 4 / 5 * 1 / 4 = 1 / 5 = 20%. Then find the probability he gets a purple egg with 5 pieces of candy the same way: 1 / 5 * 1 / 2 = 1 / 10 = 10%. Then add the probabilities of the two possible ways to get 5 pieces of candy to find the total probability: 20% + 10% = 30%. The answer is 30.
[Question]A man intends to complete a journey of 24 km in 8 hours. If he travels at a speed of 4km/hr for the first four hours, at what speed does he need to travel for the remainder of the journey to be right on time?
[Answer]He covers 4km / hr * 4hrs = 16km in the first 4 hours. He has 24 - 16 = 8km left to cover. He has 8 - 4 = 4 hours to cover the remaining 8km. He has to travel at a speed of 8km / 4hrs = 2km / hr to be right on time. The answer is 2.
Q: Cadence has worked for her new company five months longer than she worked for her old company. If she worked at her old company for 3 years earning $5000 per month, and she's now earning 20% more in the new company, calculate the total amount of money she's earned in both companies in the period she's worked for them?
A: In her old company, if she worked for three years, the total number of months she was paid for is 3 years * 12, which is the number of months in a year = 36 months. If each month she was paid $5000, her total earnings in the old company were $5000 * 36 = $180000. In her new company, she is paid 20% more, which is 20 / 100 * $5000 = $1000 per month more than what she was paid at the old company. In total, she earns $5000 + $1000 = $6000 per month in her new company. Since she's worked five months more in the new company than the old company, she has worked for 36 + 5 = 41 months in the new company. The total amount she's earned in the new company is $6000 * 41 = $246000. The combined total for both companies is $246000 + $180000 = $426000. The answer is 426000.
Question: Ronald wants to make profits by re-selling some phones he bought a week ago. He bought 200 units for just $3000, and he wants to gain a third of the initial investment in profits when all units are sold. Including the profit margin, what will be the selling price for each phone?
Answer: The profit Ronald wants is $3000 / 3 = $1000. The profit per phone sold will be $1000 / 200 phones = $5 / phone. The cost of each phone is $3000 / 200 phones = $15 / phone. The selling price including the profit will be $15 / phone + $5 / phone = $20. The answer is 20.
[Question]Fred had 236 dollars to spend on 6 books. After buying them, he had 14 dollars. On average, how much did each book cost?
[Answer]Fred spent $236 - $14 = $222 on books. The cost per book is $222 / 6 books = $37. The answer is 37.
[Question]Jerry wakes up one morning and finds the thermostat set to 40 degrees. He set it to double the initial temperature. His dad notices, yells at Jerry, and reducing the temperature by 30 degrees. Later, Jerry's mother reduces the temperature by 30%, before his sister increases it by 24 degrees. What's the final temperature?
[Answer]
First double the initial temperature: 40 degrees * 2 = 80 degrees. Then reduce that amount by 30 to reflect the dad's change: 80 degrees - 30 degrees = 50 degrees. Then multiply that number by 30% to find how much Jerry's mother reduces the temperature: 50 degrees * .3 = 15 degrees. Now subtract 15 degrees from 50 degrees to find the temperature after the mother's change: 50 degrees - 15 degrees = 35 degrees. Finally, add 24 degrees to find the final temperature: 35 degrees + 24 degrees = 59 degrees. The answer is 59.