Last month, a factory made 12000 dolls and their associated accessories. The accessories for each doll included 2 shoes, 3 bags, 1 set of cosmetics, and 5 hats. If each doll took 45 seconds to make and each accessory took 10 seconds to make, what was the total combined machine operation time, in seconds, required to manufacture all of the dolls and their accessories?

The number of shoes the factory made was 12000 dolls x 2 shoes/doll =

<<12000*2=24000>>24000 shoes The factory also made for each doll 12000 dolls x 3 bags/doll = <<12000*3=36000>>36000 bags The set of cosmetics made for each doll was just one, so there are <<12000=12000>>12000 cosmetics sets Finally, the number of hats for the dolls was 12000 dolls x 5 hats/doll = <<12000*5=60000>>60000 hats In total, the number of accessories was 24000 + 36000 + 12000 + 60000 = <<24000+36000+12000+60000=132000>>132000 accessories The dolls took in total 12000 dolls x 45 seconds/doll = <<12000*45=540000>>540000 seconds to be made All the accessories also took 132000 accessories x 10 seconds/accessory = <<132000*10=1320000>>1320000 seconds Combing both results, we have that the total time the machinery was working was 1320000 + 540000 = <<1320000+540000=1860000>>1860000 seconds #### 1860000 A monkey swings from branch to branch at an average distance of 1.2 meters per second. How far will a monkey swing in meters if it consistently swings from branches for 30 minutes? If a monkey swings 1.2 meters a second then a monkey can swing 1.2 meters/second * 60 seconds/minute = <<1.2*60=72>>72 meters in a minute. If a monkey swings 72 meters in a minute then a monkey can swing 72 meters/min * 30 minutes = <<72*30=2160>>2,160 meters in 30 minutes #### 2160 Lucca has 100 balls and 10 percent of his balls are basketballs. Lucien has 200 balls and 20 percent of them are basketballs. In total how many basketballs do Lucca and Lucien have? Lucca has 100 basketballs x (10 / 100) = <<100*10/100=10>>10 basketballs. Lucien has 200 basketballs x (20 / 100) = <<200*(20/100)=40>>40 basketballs Together they have 10 basketballs + 40 basketballs = <<10+40=50>>50 basketballs. #### 50 Out of 804 senior high school students, 75% passed their exams and so got their degree. The rest failed. How many didn't pass their exams? Find the number of students who got their degree by multiplying: 804 students * 75% = <<804*75*.01=603>>603 students. Then find the number of students who didn't pass their exams by subtracting this number from the total: 804 students - 603 students = <<804-603=201>>201 students. #### 201 A tiger shark has 180 teeth. A hammerhead shark has 1/6 the number of teeth that a tiger shark has. A great white shark has double the sum of teeth of a tiger shark and a hammerhead shark. How many teeth does a great white shark have? Hammerhead shark:180/6=<<180/6=30>>30 Great White:2(180+30)=420 teeth #### 420 A group of researchers are studying a colony of penguins. Their results show that the size doubled in the first year they watched the colony, then tripled in the next year. This year, however, harsh conditions meant the colony only gained 129 penguins. The colony has 1077 penguins in it now. Each penguin eats one and a half fish every day. How many fish did the whole colony catch per day to eat at the beginning of the first year? The colony had 1077 - 129 = <<1077-129=948>>948 penguins in it at the beginning of this year. At the beginning of the second year, the colony had 948 / 3 = <<948/3=316>>316 penguins in it. At the beginning of the first year, it had 316 / 2 = <<316/2=158>>158 penguins in it. Thus, at the beginning of the first year, the penguin colony was catching 158 * 1 1/2 = 237 fish per day. #### 237 Five less than three times the number of Doberman puppies plus the difference between the number of Doberman puppies and the number of Schnauzers is equal to 90. If the number of Doberman puppies is 20, how many Schnauzers are there? Three times the number of Doberman puppies is 3*20=<<3*20=60>>60 Five less than three times the number of Doberman puppies is 60-5=<<60-5=55>>55 Let's say the number of Schnauzers is s. The difference between the number of Doberman puppies and the number of Schnauzers is s-20 Five less than three times the number of Doberman puppies plus the difference between the number of Doberman puppies and the number of Schnauzers is equal to 90, meaning 55+s-20=90. The number of Schnauzers which is s+55-20=90 This evaluates to s+35=90 There are s=<<55=55>>55 Schnauzers #### 55 In 5 years, Heath will be 3 times as old as Jude. If Heath is 16 years old today, how old is Jude today? In 5 years, Heath will be 16 + 5 = <<16+5=21>>21 years old. In 5 years, Jude will be 21 / 3 = <<21/3=7>>7 years old. The difference in their ages is 21 - 7 = <<21-7=14>>14 years. Today, Jude will be 16 - 14 = <<16-14=2>>2 years old. #### 2 A store is comparing their profits throughout the year. They had profits of $1,500 in the first quarter of the year, $3,000 in the third quarter, and $2,000 in the fourth quarter. If their annual profits are $8,000, how much profit, in dollars, did they make in the second quarter? In the three quarters we have figures for, the store made a total of $1500 + $3000 + $2000 = $<<1500+3000+2000=6500>>6,500. Subtracting this from their annual profit shows that they made $8000 – $6500 = $<<8000-6500=1500>>1,500 profit in the second quarter. #### 1500 A van is delivering 180 bottles of drinks to a neighborhood, and each bottle contains either cider or beer or a mixture of two. Out of the 180 bottles, 40 contain only cider, 80 contain only beer, and the rest are a mixture of the two drinks. If the delivery man gives half the number of each bottle of drink to the first house, how many bottles does the first house get? The total number of bottles containing cider or beer is 40+80 = <<40+80=120>>120 If the number of bottles in the van was 180, then 180-120 =<<180-120=60>>60 contains a mixture of the two drinks. At the first house, the delivery man dropped 1/2*40 = <<1/2*40=20>>20 bottles. There were also 1/2*80 = <<1/2*80=40>>40 bottles of beer that the delivery man gave to the first house. Together, the first house received 40+20 = <<40+20=60>>60 bottles of cider and beer The total number of bottles that had a mixture of the two drinks that were dropped at the first house is 1/2*60 = <<1/2*60=30>>30 The first house got 60+30 = <<60+30=90>>90 bottles of all types of drinks. #### 90