[Question]Bob wants to build a pyramid out of legos with 3 levels where the bottom level has 7 legos per side and each level has one less lego per side than the level below it. How many legos total will he need?
[Answer]First find the total number of legos on the bottom layer: 7 legos * 7 legos = 49 legos. Then find the number of legos per side on the next layer: 7 legos - 1 lego = 6 legos. Then find the total number of legos on the second level: 6 legos * 6 legos = 36 legos. Then find the number of legos per side on the top level: 6 legos - 1 lego = 5 legos. Then find the total number of legos on the top level: 5 legos * 5 legos = 25 legos. Then add the number of legos on each level to find the total number of legos: 49 legos + 36 legos + 25 legos = 110 legos. The answer is 110.
Q: A farm has 5 less than 9 times the amount of hens as roosters. If there are 75 total chickens, how many hens are there?
A: Let x represent the number of roosters. Number of hens:9x - 5. Total:9x - 5 + x = 75. 10x - 5 = 75. 10x = 80. x = 8. Number of hens: 9(8) - 5 = 67. The answer is 67.
Question: At the museum, Bethany saw 4 times more still lifes than portraits. If she saw 80 paintings total, how many portraits did she see?
Answer: Let s be the number of still lifes Bethany saw and p be the number of portraits. We know that s + p = 80 and s = 4p. Substituting the second equation into the first equation, we get 4p + p = 80. Combining like terms, we get 5p = 80. Dividing both sides by 5, we get p = 16. The answer is 16.
[Question]Mary is trying to count the animals in the petting zoo, but they kept moving around so she double-counts 7 sheep and forgets to count 3 pigs. If Mary thinks there are 60 animals, how many are there really?
[Answer]First subtract the 7 double - counted animals from Mary's total: 60 animals - 7 animals = 53 animals. Then add the animals she missed to find the real total: 53 animals + 3 pigs = 56 animals. The answer is 56.
Q: Nicky is trading baseball cards with Jill. If Nicky trades two cards worth $8 each for 1 card worth $21, how many dollars of profit does he make?
A: First find the total cost of the two $8 cards: $8 / card * 2 cards = $16. Then subtract the cost of the cards Nicky gave away from the cost of the card he received to find his profit: $21 - $16 = $5. The answer is 5.
Question: In one week, Jake can eat 3 papayas, his brother can eat 5 papayas, and his father can eat 4 papayas. To account for 4 weeks, how many papayas does Jake need to buy from the farmer's market?
Answer:
In one week, the 3 men can eat 3 + 5 + 4 = 12 papayas. For 4 weeks, Jake will need to buy 12 x 4 = 48 papayas. The answer is 48.