In a factory, there are 3 machines working 23 hours a day. The owner decided to buy a fourth machine, which works only 12 hours a day. One machine can produce 2 kg of material every hour. The factory sells the produced material for $50 per 1 kg. How much can this factory earn in one day?

The total runtime for the first three machines is 3 machines * 23 hours/day/machine =

<<3*23=69>>69 hours/day. So these machines could produce 69 hours/day * 2 kg/hour = <<69*2=138>>138 kg/day. The fourth machine could produce 12 hours/day * 2 kg/hour = <<12*2=24>>24 kg/day of material. In total all the machines would produce 138 kg/day + 24 kg/day = <<138+24=162>>162 kg/day of material. The factory would therefore earn 162 kg/day * $50/kg = $<<162*50=8100>>8100/day. #### 8100 Amalia can read 4 pages of her book in 2 minutes. How many minutes will it take her to read 18 pages of her book? Amalia can read 1 page in 2/4 = 0.5 minutes. Hence, she can read 18 pages in 18 x 0.5 minutes = <<18*0.5=9>>9 minutes. #### 9 In a 60-item exam, Liza got 90% of the items correctly. Her best friend, Rose, got 2 more correct answers than her. How many incorrect answers did Rose have? Liza got 60 x 90/100 = <<60*90/100=54>>54 of the items correctly. So, Rose got 54 + 2 = <<54+2=56>>56 of the items correctly. Thus, Rose had 60 - 56 = <<60-56=4>>4 incorrect answers. #### 4 Harry participates in the auction of a classic painting. The auction starts at $300, Harry is the first to bid, adding $200 to the starting value, a second bidder doubles the bid, and a third bidder adds three times Harry's bid. Finally, Harry bids $4,000. By how much did Harry's final bid exceed that of the third bidder? Adding Harry's $200 to the initial value, the bid is at 300 + 200 = $<<300+200=500>>500. The second bidder doubles the previous value, reaching a value of 500 * 2 = $<<500*2=1000>>1000. The third bidder adds three times the value of Harry's, then adds 500 * 3 = $<<3*500=1500>>1500 Adding the $1500 to the value of the second bid, the bid is at 1500 + 1000 =$<<1500+1000=2500>>2500. With the final bid of $4000, Harry bids 4000 - 2500 = $<<4000-2500=1500>>1500 more than the third bidder. #### 1500 Martha is knitting winter clothes for her 3 grandchildren, who are all the same size (identical triplets.) Each set of clothes consists of a woolen hat, a scarf, a sweater, a pair of mittens, and a pair of wooly socks. She can knit a hat in 2 hours. A scarf takes her 3 hours. Each mitten takes her about an hour to knit. A sock takes an hour and a half. Each sweater takes her 6 hours. How long will it take her to knit all the outfits? A pair of mittens takes 1 hour per mitten * 2 mittens = <<1*2=2>>2 hours. A pair of socks takes 1.5 hours per sock * 2 socks = <<1.5*2=3>>3 hours. So a complete outfit for each child takes 2 hours per hat + 3 hours per scarf + 2 hours per pair of mittens + 3 hours per pair of socks + 6 hours per sweater = <<2+3+2+3+6=16>>16 hours per outfit. So to knit winter outfits for all three of her grandchildren, Martha will take 3 outfits * 16 hours per outfit = <<3*16=48>>48 hours. #### 48 A city has a population of 300,000. 50,000 people immigrate to the country and then 30,000 people leave. After that 1/8 of the population gets pregnant and 1/4 of those people have twins. How many people are there after the births? There was a net immigration to the country of 50,000-30,000=<<50000-30000=20000>>20,000 So the total number of people before birth is 300,000+20,000=<<300000+20000=320000>>320,000 That means 320,000/8=<<320000/8=40000>>40,000 get pregnant So 40,000/4=<<40000/4=10000>>10,000 have twins So that means they have 10,000*2=<<10000*2=20000>>20,000 children There are 40,000-10,000=<<40000-10000=30000>>30,000 children from single births So the total number of people is 320,000+30,000+20,000=<<320000+30000+20000=370000>>370,000 #### 370000 The number of female students in the school hall is 4 times as many as the number of male students. If there are 29 male students, and there are 29 benches in the hall, at least how many students can sit on each bench for them to all fit in the hall? The number of female students is 4 times 29: 4*29 = <<4*29=116>>116 There are a total of 29+116 = <<29+116=145>>145 students in the hall There are 29 benches so each bench should take 145/29 = 5 students #### 5 The first store charges $3 for 6 apples while the second store charges $4 for 10 apples. How many cents can you save on each apple from buying $4 for 10 apples than from $3 for 6 apples? In the first store, each apple costs $3/6 = $<<3/6=0.5>>0.5. In the second store, each apple costs $4/10 = $<<4/10=0.4>>0.4. So, you can save $0.5 - $0.4 = $0.1 on each apple from buying $4 for 10 apples than from $3 for 6 apples. In cents, this is equal to $0.1 x 100 = <<0.1*100=10>>10. #### 10 Ishmael was monitoring whales out at sea for conservation purposes. Each time he takes a trip to sea, he sees a different group of whales. On his first trip, he counts 28 male whales and twice as many female whales. On his second trip, he sees 8 baby whales, each travelling with their parents. On his third trip, he counts half as many male whales as the first trip and the same number of female whales as on the first trip. In total, how many whales were out at sea during Ishmael’s monitoring? On the first trip, Ishmael sees 28 male whales * 2 = <<28*2=56>>56 female whales. So in total, he sees 28 male whales + 56 female whales = <<28+56=84>>84 whales on the first trip. On the second trip, each baby whale travels with its parents which means it travels in a group of 1 baby whale + 2 parents = <<1+2=3>>3 whales/baby whale. This means there are 8 baby whales * 3 whales/baby whale = <<8*3=24>>24 whales on the second trip. On the third trip, there are half as many male whales as there were on the first trip, so there must be 28 male whales / 2 = <<28/2=14>>14 male whales. Adding this to the female whales means he saws 14 males whales + 56 female whales = <<14+56=70>>70 whales on the third trip. In total, Ishmael saw 84 + 24 + 70 = <<84+24+70=178>>178 whales across the three trips. #### 178 Brenda catches smallpox. She has 60 blisters on each arm and 80 blisters on the rest of her body. How many blisters does she have in total? First find the total number of blisters on Brenda's arms: 60 blisters/arm * 2 arms = 120 blisters Then add the blisters on the rest of her body to find the total: 120 blisters + 80 blisters = <<120+80=200>>200 blisters #### 200