Ellie went to visit a circus with Sarah and they both got lost in the house of mirrors. They have to travel through the house of mirrors a few times before they finally get out and when they leave, they discuss how many times they've seen their own reflections. Sarah says that every time they were in the room with tall mirrors, she saw her reflection 10 times and every time they were in the room with wide mirrors, she saw her reflection 5 times. Ellie says that every time they were in the room with tall mirrors, she saw her reflection 6 times and every time they were in the room with wide mirrors she saw her reflection 3 times. They both passed through the room with tall mirrors 3 times each and they both passed through the room with wide mirrors 5 times each. In total, how many times did Sarah and Ellie see their reflections?

How many times did Sarah see her reflection in the rooms with tall mirrors? ** In the rooms with tall mirrors, Sarah saw her reflection a total of 10 reflections * 3 passes =

<<10*3=30>>30 times. How many times did Sarah see her reflection in the rooms with wide mirrors? ** In the rooms with wide mirrors, Sarah saw her reflection a total of 5 reflections * 5 passes = <<5*5=25>>25 reflections. How many times did Sarah see her reflection? ** So Sarah saw her reflection a total of 30 + 25 = <<30+25=55>>55 times. How many times did Ellie see her reflection in the rooms with tall mirrors? ** In the rooms with tall mirrors, Ellie saw her reflection a total of 6 reflections * 3 passes = <<6*3=18>>18 times. How many times did Ellie see her reflection in the rooms with wide mirrors? ** In the rooms with wide mirrors, Ellie saw her reflection a total of 3 reflections * 5 passes = <<3*5=15>>15 times. How many times did Ellie see her reflection? ** So Ellie saw her reflection a total of 18 + 15 = <<18+15=33>>33 times. How many times did Sarah and Ellie see their reflections? ** Therefore, Sarah and Ellie saw their reflections a total of 55 + 33 = <<55+33=88>>88 times. #### 88 Kenny wants to make sure he does more jumping jacks every week than he did the week before. He recorded that last week he did 324 total jumping jacks. On Saturday of this week, he looks at his records and sees that on Sunday he did 34. On Monday he did 20. On Tuesday he skipped a day. On Wednesday he did 123. On Thursday he did 64. On Friday he did 23. How many does he have to do on Saturday to make sure he beats last week's number? How many has Kenny done this week? ** He has already done 264 this week because 34 + 20 + 123 + 64 + 23 = <<34+20+123+64+23=264>>264. How many does Kenny have to do on Saturday to make sure he beats last week's number? ** If he does 60 he will have done as many as last week because 324 - 264 = <<60=60>>60 How many does Kenny have to do on Saturday? ** He has to do 61 on Saturday because 60 + 1 = <<60+1=61>>61 #### 61 In a field of 500 clovers, 20% have four leaves and one quarter of these are purple clovers. Assuming these proportions are exactly correct, how many clovers in the field are both purple and four-leaved? How many four leaf clovers are there? ** There are 500/5= <<500/5=100>>100 four leaf clovers How many purple four leaf clovers are there? ** There are 100/4= <<100/4=25>>25 purple four leaf clovers #### 25 Edna made cookies for all of her neighbors and left the cookies outside for them to take. She made 150 cookies so her 15 neighbors could get 10 cookies each. However, the neighbor who arrived last told Edna there were only 8 cookies left. Edna thinks it was Sarah who took too many cookies. If all the other neighbors took the correct amount of cookies, how many cookies did Sarah take? How many cookies did the other neighbors take? ** Sarah and the final neighbor took the wrong amount, which means that 15 neighbors – 1 Sarah – 1 final neighbor = 13 neighbors took 10 cookies each. How many cookies did the first 13 neighbors take? ** This is a total of 13 neighbors * 10 cookies = <<13*10=130>>130 cookies taken by the first 13 neighbors. How many cookies did the first 13 neighbors and Sarah take? ** There were only 8 cookies left, so that means the first 13 neighbors and Sarah took a total of 150 – 8 = 142 cookies. How many cookies did Sarah take? ** So Sarah must have taken 142 – 130 = <<142-130=12>>12 cookies. #### 12 John builds a box. The box is 26 inches by 26 inches by 14 inches. The walls are 1 inch thick on each side. How much is the internal volume in cubic feet? How many inches are the walls? ** The walls take away 2*1=<<2*1=2>>2 inches from each dimension How long are the longer sides? ** So the longer sides are 26-2=<<26-2=24>>24 inches How long are the longer sides? ** That is 24/12=<<24/12=2>>2 feet How small is the smaller dimension? ** The smaller dimension is 14-2=<<14-2=12>>12 inches How small is the smaller dimension? ** That is 12/12=<<12/12=1>>1 foot How much is the internal volume in cubic feet? ** So the internal volume is 2*2*1=<<2*2*1=4>>4 cubic feet #### 4 Tommy has 10 more sheets than Jimmy does. If Jimmy has 32 sheets, how many more sheets will Jimmy have than Tommy if his friend Ashton gives him 40 sheets. How many sheets does Tommy have? ** If Jimmy has 32 sheets, and Tommy has 10 more sheets than Jimmy does, Tommy has 10+32 = <<32+10=42>>42 sheets. How many sheets does Jimmy have after Ashton gives him 40 sheets? ** When Ashton gives Jimmy 40 sheets, his total number of sheets increases to 32+ 40 = <<32+40=72>>72 How many more sheets does Jimmy have than Tommy? ** The number of sheets that Jimmy now have than Tommy is 72-42 = <<72-42=30>>30 #### 30 A book has 8 chapters. Beth has read 2 chapters in 3 hours. If she continues reading at that rate, in how many hours will she be able to finish reading the remaining chapters? How many chapters does Beth still need to read? ** Beth still needs to read 8 - 2 = <<8-2=6>>6 chapters. How many hours does it take Beth to read a chapter? ** She can read 1 chapter in 3/2 = <<1.5=1.5>>1.5 hours. How many hours will Beth be able|endoftext|>|endoftext|>|endoftext|>|endoftext|>|endoftext|>|endoftext|>|endoftext|>| ** Therefore, she will be able to finish reading the remaining chapters in 1.5 x 6 = <<1.5*6=9>>9 hours. #### 9 Bob is building a garden on his land, and he wants it to be fenced in to keep out varmints. The garden is a rectangular plot 225 feet long by 125 feet wide. He also wants to have a small 3-foot wide gate to walk through and a larger 10-foot wide gate to move his gardening equipment through. How much fencing is Bob going to need to fence in his garden, taking into account the two gates? How many feet is the perimeter of the garden? ** The perimeter of the garden is 2 * 225 + 2 * 125 = 450 + 250 = <<2*225+2*125=700>>700 feet. How many feet of fencing does Bob need? ** Minus the two gates, he will need at least 700 - 3 - 10 = <<687=687>>687 feet of fencing. #### 687 Abe owns a restaurant. Every month he spends a third of his budget on food, a quarter of his budget on restaurant supplies, and the rest of his budget on employee wages. If his budget is $3000 and he uses it up every month, how much is he spending on wages? How much is Abe spending on food? ** Abe is spending a third of his budget on food, so he spends $3000 / 3 = $<<3000/3=1000>>1000 on food. How much is Abe spending on supplies? ** He spends a quarter of his budget on restaurant supplies, so he spends $3000 / 4 = $<<3000/4=750>>750 on supplies. How much is Abe spending on wages? ** Thus, he spends $3000 - $1000 - $750 = $<<3000-1000-750=1250>>1250 on employee wages every month. #### 1250 Holly wants to plant a wall of privacy trees along her fence line. Her fence is 25 yards long. At maturity, the trees she wants to plant will measure 1.5 feet wide. Right now, these trees are on sale for $8.00 apiece. How much will it cost her to plant a row of the trees to run the length of her fence? How long is her fence? ** 3 feet are in 1 yard and her fence is 25 yards long so her fence is 3*25 = <<3*25=75>>75 feet long How many trees does she need? ** At maturity these trees will measure 1.5 feet and she needs them to run along her 75-foot fence so she needs 75/1.5 = <<75/1.5=50>>50 trees How much will it cost her to plant a row of the trees to run the length of her fence? ** The trees cost $8.00 apiece and she needs 50 so 8*50 = $<<8*50=400.00>>400.00 worth of trees #### 400