Carolyn is planning out her final essay. The introduction will be 450 words, the conclusion will be triple the length of the introduction, and each of the four body sections will be the same length. If her essay has to be 5000 words total, how long is each section?

First find the length of the conclusion by tripling the length of the introduction: 450 words * 3 =

<<450*3=1350>>1350 words Then subtract the length of the introduction and conclusion from the total length to find the combined length of the body sections: 5000 words - 1350 words - 450 words = <<5000-1350-450=3200>>3200 words Then divide the combined length of the body section by the number of body sections to find the length of each section: 3200 words / 4 sections = <<3200/4=800>>800 words/section #### 800 Sophie buys five cupcakes at $2 each, six doughnuts at $1 each, four slices of apple pie at $2 per slice, and fifteen cookies at $0.60 each. How much does she spend in all? Five cupcakes cost 5 x $2 = $<<5*2=10>>10. Six doughnuts cost 6 x $1 = $<<6*1=6>>6. Four slices of apple pie cost 4 x $2 = $<<4*2=8>>8. And, fifteen cookies cost 15 x $0.60= $<<15*0.60=9>>9. Therefore, Sophie spends $10 + $6 + $8 + $ 9 = $<<10+6+8+9=33>>33. #### 33 Tod drives his family car 55 miles to the north and 95 miles to the west. If Tod constantly drives 25 miles an hour the entire trip how many hours did Tod drive? 55 miles north and 95 miles west give 55+95=<<55+95=150>>150 miles total 150 miles at 25 miles an hour gives 150/25=<<150/25=6>>6 hours #### 6 Savannah is wrapping presents for her friends and family for Christmas. She has bought 3 rolls of wrapping paper to wrap 12 gifts. If it takes 1 roll to wrap 3 gifts and 1 roll to wrap 5 other gifts, if there is no wrapping paper leftover after Savannah wraps the rest of the gifts, how many gifts did she wrap with the third roll of paper? Savannah has 12 gifts to give her friends and family and has already wrapped 3 gifts + 5 gifts = 8 gifts already wrapped with the first two rolls of paper. She started off with 12 gifts to wrap and has already wrapped 8, 12 - 8 = <<12-8=4>>4 gifts she wraps with the third roll of paper. #### 4 Sedrach has 13 apple pies. If every apple pie can be quickly divided into halves and every half an apple pie can be split into 5 bite-size samples, how many people can taste Sedrach's apple pie if he divides them all into bite-size samples? Every apple pie has 5 x 2 = <<5*2=10>>10 bite sizes 13 x 10 = <<13*10=130>>130 people can taste Sedrach's apple pies #### 130 One student on a field trip counted 12 squirrels. Another counted a third more squirrels than the first student. How many squirrels did both students count combined? The second student counted 12/3 = 4 more squirrels than the first student. The second student counted 12+4 = <<12+4=16>>16 squirrels. Together, the first and second student counted 12+16 = <<12+16=28>>28 squirrels combined. #### 28 The teacher told the class that if they averaged at least 75% on their final exam, they could have a pizza party. Everyone took the exam on Monday, except for William, who was allowed to take it on Tuesday. If there are 30 people in the class, and the average before he took the test was a 74%, what score does he have to get to make sure they get to have a pizza party? Let x be the score that William needs to achieve. Since there are 30 people in the class, there are 30 - 1 = <<30-1=29>>29 people without him. Since their average was a 74%, this means that (29 * 74 + x) / 30 >= 75. Thus, 29 * 74 + x >= 30 * 75 Thus, 29 * 74 + x >= 2250 Thus, 2146 + x >= 2250 Thus, x >= 2250 - 2146 Thus, x >= 94 #### 94 A school is getting ready to open for the year and the sports class is organizing the equipment they have been donated. In total, they have 300 donations to organize. 60 of these were basketball hoops, half of which also had basketballs included as part of the donation. 120 pool floats were donated, but a quarter of these were damaged and were discarded before the sports class arrived. There were 50 footballs, 40 tennis balls, and the remaining donations were basketballs. In total, how many basketballs have been donated? Some of the pool floats were damaged, which means that 120 / 4 = <<120/4=30>>30 pool floats were discarded. This left the class with 120 – 30 = <<120-30=90>>90 pool floats that were actually part of the donations they need to organize. This means there were a total of 60 basketball hoops + 90 pool floats + 50 footballs + 40 tennis balls = <<60+90+50+40=240>>240 donations that were not basketballs. So out of the donations, there were 300 donations – 240 = <<300-240=60>>60 basketballs. In addition, half of the basketball hoops were donated with a basketball included which amounts to 60 basketball hoops / 2 = <<60/2=30>>30 basketballs. There was therefore a total of 60 + 30 = <<60+30=90>>90 basketballs donated. #### 90 Dorothy spent $53 to buy doughnut ingredients. If she made 25 doughnuts and sells each for $3, how much was her profit? She was able to earn 25 x $3 = $<<25*3=75>>75 for the doughnuts. Therefore, Dorothy's profit is $75 - $53 = $<<75-53=22>>22. #### 22 Gavin has had 4 dreams every day for a year now. If he had twice as many dreams last year as he had this year, calculate the total number of dreams he's had in the two years. Since a year has 365 days, if Gavin has been having 4 dreams every day for a year now, he has had 4*365 = <<4*365=1460>>1460 dreams this year. Gavin had twice as many dreams last as he had this year, meaning he had 2*1460 = <<2*1460=2920>>2920 dreams last year. The total number of dreams he has had in the two years is 2920+1460=<<2920+1460=4380>>4380 dreams. #### 4380