Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need?

We know that the top level just has one case. Since each level has one more case per side than the level above it, the second level has sides that are 2 cases long.

We can figure out how many cases we need for the second level by finding the area of a square with a side length of 2: 2 cases * 2 cases =

<<2*2=4>>4 cases The third level has three cases per side, so we need to find the area of a square with side length 3: 3 cases * 3 cases = <<3*3=9>>9 cases The fourth level has a side length of 4, so we find its area with 4 cases * 4 cases = <<4*4=16>>16 cases Finally, we add up the number of cases we need on each level: 1 cases + 4 cases + 9 cases + 16 cases = <<1+4+9+16=30>>30 cases #### 30 Peter knows that the distance an airplane travels between Spain and Russia is 7019 km, while the distance between Spain and Germany is 1615 km. Peter took a flight from Spain, which made a stopover in Germany, while being there, he receives a call from his brother asking him how many kilometers he has to fly to get to Russia and then return to Spain. What will Peter answer? Being 7019 km the distance from Spain to Russia. To get from Germany to Russia, Peter has to travel 7019 - 1615 = <<7019-1615=5404>>5404 km Knowing both distances, Peter will answer that he has to fly 5404 + 7019 = <<5404+7019=12423>>12423 km #### 12423 John has to replace the ball bearings for machines he works with. He has 10 machines and they take 30 ball bearings each. It normally costs $1 per ball bearing but right now there is a sale where they are only $.75. Also since he is buying in bulk he gets a further 20% discount. How much money did he save by buying them all during the sale rather than 1 at a time? He needs to replace 30*10=<<30*10=300>>300 ball bearings The normal price is 300*1=$<<300*1=300>>300 Because of the sale he only has to pay 300*.75=$<<300*.75=225>>225 He then gets a discount which shaves another 225*.2=$<<225*.2=45>>45 off the price That means he only pays 225-45=$<<225-45=180>>180 So he saved 300-180=$<<300-180=120>>120 #### 120 Each slice of cheesecake contains 350 calories. If there are a total of 2800 calories in every cheesecake, and Kiley ate 25% of the cheesecake, how many slices of cheesecake did Kiley eat? If there are 2800 calories in every cheesecake, and each slice of cheesecake contains 350 calories, then the cheesecake has 2800/350=<<2800/350=8>>8 slices. If Kiley ate 25% of the cheesecake, then she ate 8*0.25=<<8*0.25=2>>2 slices of cake. #### 2 Sara's sister has 4 small notebooks in her closet. Last summer she ordered 6 more notebooks and then lost 2. How many notebooks does Sara's sister have now? Sara's sister has 4 + 6 = <<4+6=10>>10 notebooks. After she loses 2, she will have: 10 - 2 = <<10-2=8>>8 notebooks. #### 8 Meadow has a business that sells baby diapers to her local townspeople. She orders 30 boxes of diapers containing 40 packs weekly, with each pack having 160 diapers. She sells each diaper for $5. How much money is Meadow making from selling all her diapers? When she orders 30 boxes, the total number of packs in the boxes is 30*40 = <<30*40=1200>>1200 packs. If a pack has 160 diapers, 1200 packs contain 1200*160 = <<1200*160=192000>>192000 diapers. After selling all the diapers, Meadow gets 192000*$5 = $<<192000*5=960000>>960000 #### 960000 Lilith is trying to break the world record for largest cap collection. She collects 3 caps per month in the first year, and 5 caps per month after the first year. Each Christmas, she also receives 40 caps from friends and family. She estimates that each year, she loses 15 of the caps she has collected. If Lilith has been collecting for 5 years, how many caps has she collected so far? In the first year, Lilith collects 3 caps * 12 months = <<3*12=36>>36 caps. Every year afterwards, she collects 5 caps * 12 months = <<5*12=60>>60 caps. She does this for a total of 5 – 1 = <<5-1=4>>4 years. This is a total of 60 caps * 4 years = <<60*4=240>>240 caps. In total, she collects 36 + 240 = <<36+240=276>>276 caps by herself. Over the Christmases, she receives 40 caps * 5 years = <<40*5=200>>200 caps from friends and family. She also loses 15 caps * 5 years = <<15*5=75>>75 caps over the years. She has therefore collected 276 + 200 – 75 = <<276+200-75=401>>401 caps. #### 401 A quarterback steps back to throw 80 times in a game. 30 percent of the time he does not get a pass thrown. Half of the times that he does not throw the ball he is sacked for a loss. How many times is the quarterback sacked for a loss in the game? No pass thrown:80(.30)=24 Sacked:24/2=<<24/2=12>>12 #### 12 Three years ago, Bethany was twice the age of her younger sister. In 5 years, her younger sister will be 16. How old is Bethany now? First find how old Bethany's sister currently is: 16 years - 5 years = <<16-5=11>>11 years Then find how old her sister was 3 years ago: 11 years - 3 years = <<11-3=8>>8 years Then double that age to find how old Bethany was three years ago: 8 years * 2 = <<8*2=16>>16 years Then add 3 years to that number to find how old Bethany is now: 16 years + 3 years = <<16+3=19>>19 years #### 19 During the Christmas holidays, all shops are closed for 3 days. During each day during this time, a shop called "Surprise" could have earned 5 thousand dollars. How much potential revenue did the "Surprise" shop lose during 6 years of activity? In one day the shop is losing 5 thousand dollars, so during three days, the losses are 5 * 3 = $15,000. Christmas holidays are once a year, so in 6 years the shop "Surprise" could have earned another $15,000 * 6 = $<<6*15000=90000>>90,000. #### 90,000