James decides to try and collect rare artifacts in the field. He spends 6 months researching before going on a 2-year-long expedition for his first find. The second artifact takes 3 times as long for the research and discovery. How long did it take him to find both?

The research took 6/12=

<<6/12=.5>>.5 years So it took 2+.5=<<2.5=2.5>>2.5 years for the first artifact It takes 2.5*3=<<2.5*3=7.5>>7.5 years for the second So in total it took 2.5+7.5=<<2.5+7.5=10>>10 years to find both #### 10 Jonathan eats 2500 calories every day except for Saturday, when he consumes an extra 1000 calories. He burns 3000 calories every day. What is his weekly caloric deficit? He consumes 2500+1000=<<2500+1000=3500>>3500 calories on Saturday He consumes 2500*6+3500=<<2500*6+3500=18500>>18500 calories in the week. He burns 3000*7=<<3000*7=21000>>21000 calories in the week His caloric deficit is 21000-18500=<<21000-18500=2500>>2500 calories per week #### 2500 John uses a 75-watt electric fan for 8 hours a day. How much kWh of electric energy does he consume per month (30 days) for using the electric fan? In a day, John uses 75x 8 = <<75*8=600>>600 watts. So in a month, he uses 600 x 30 = 18 000 watts. Since there are 1000 watts in 1 kilowatt, then John uses 18000/1000 = <<18000/1000=18>>18. #### 18 Alexandra bought 8 magazines at the bookstore on Friday. On Saturday, she went back and bought 12 more. Sunday morning, she saw that the store was having a sale and she bought four times the number of magazines she did on Friday. Later that day she discovered that her dog had chewed up 4 of the magazines. How many magazines does she have now? By adding Friday and Saturday, Alexandra bought 12+8=<<12+8=20>>20 magazines On Sunday she buys 8*4=<<8*4=32>>32 magazines Before her dog got to them she had 12+8+32=<<12+8+32=52>>52 magazines After her dog chewed up some she had 52-4=<<52-4=48>>48 magazines #### 48 A state fair charges $5 for a ticket. Two-thirds of the people who buy a ticket will buy deep-fried fair food for $8, one quarter will go on a ride for $4, and one eighth will spend $15 on a souvenir. The fair made $2520 from tickets. How many dollars did they make in all? The fair made $2520 from tickets, so they had 2520 / 5 = <<2520/5=504>>504 people attend the fair. Two-thirds of those people will buy food, so 504 * 2 / 3 = <<504*2/3=336>>336 people will buy food. The fair will make 336 * 8 = $<<336*8=2688>>2688 from food. A quarter of the people will go on a ride, so 504 / 4 = <<504/4=126>>126 people will go on a ride. The fair will make 126 * 4 = $<<126*4=504>>504 from rides. An eighth of the people will buy a souvenir, so 504 / 8 = <<504/8=63>>63 people will buy souvenirs. The fair will make 63 * 15 = $<<63*15=945>>945 from souvenirs. In all, the fair will make 2520 + 2688 + 504 + 945 = $<<2520+2688+504+945=6657>>6657. #### 6657 Lana and Mike are taking their dog and renting a cabin in the mountains for 2 weeks. The daily rate is $125.00 There is a $100.00 pet fee. There is also a 20% service/cleaning fee for the rental. They need to pay 50% of the entire bill as a security deposit. How much is their security deposit? There are 7 days in a week and they're going for 2 weeks so that's 7*2 = <<7*2=14>>14 days The daily rate is $125.00 and they are staying for 14 days so that's 125*14 = $<<125*14=1750.00>>1,750.00 There is also a $100.00 pet fee on top of their rental fee of $1,750.00 so that's 100+1750 = $<<100+1750=1850.00>>1850.00 There is a 20% fee on the $1,850.00 so the fee comes to .20*1850 = $370.00 The rental will costs $1,850.00 and there is $370.00 service/cleaning fee for a total of 1850+370 = $<<1850+370=2220.00>>2,220.00 They need to pay 50% of the entire bill as a security deposit so that will be .5*2220 = $<<50*.01*2220=1110.00>>1,110.00 #### 1110 Ali, Peter, and Joey were fishing. The fish Ali caught weighed, in sum, twice as much as the fish that Peter caught. Joey caught 1 kg more fish than Peter. Together the three of them caught 25 kg of fish. How many kilograms did Ali catch? Let x be the weight of the fish that Peter caught. Then Ali and Joey caught 2*x and x+1 kg of fish, respectively. So, x+ 2*x + x+1 =25 So, 4*x = 25 - 1 = 24 So, x = <<6=6>>6 Therefore, Ali caught 2*x = 2*6 = 12 kg of fish #### 12 A forester is planting trees. The forest already has 30 native trees. On Monday he triples the number of total trees in the forest by planting new trees. On Tuesday, he plants a third of the amount he planted on Monday. How many trees has the forester planted in total? Let M be the number of trees he plants on Monday. On Monday the forest was three times larger from the trees that were originally there and the M trees: 3*30 = 30 + M trees. So, 90=30+M. And, M = <<60=60>>60 trees. On Tuesday, he planted 60 trees / 3 = <<60/3=20>>20 trees. In total, he has planted 60 trees + 20 trees = <<60+20=80>>80 trees. #### 80 Roy has 2 blue pens. He has twice as many black and 2 less than twice as many red than black pens. How many pens does Roy have in all? Roy has 2 x 2 = <<2*2=4>>4 black pens. Twice the number of black pens is 4 x 2 = <<4*2=8>>8. So, there are 8 - 2 = <<8-2=6>>6 red pens. Therefore, Roy has 2 + 6 + 4 = <<2+6+4=12>>12 pens in all. #### 12 Devin teaches one math course per year. He taught Calculus for 4 years, Algebra for twice as many years, and Statistics for 5 times as long as he taught Algebra. How many years has Devin taught? Calculus: <<4=4>>4 years Algebra: 4(2)=8 years Statistics: 8(5)=<<8*5=40>>40 years Total number of years taught: 4+8+40=<<4+8+40=52>>52 years #### 52