4 students participated in a 200m race. If the average completion time of the last three students was 35 seconds, and the average completion time of all four runners was 30 seconds, how long (in seconds) did it take the student who came first to finish the race?

The last 3 students had an average completion time of 35 seconds so the sum of their completion times was 3*35 =

<<3*35=105>>105 seconds All 4 students (now including the student who came first) had an average completion time of 30 seconds, meaning the sum of their completion times is 4*30 = <<4*30=120>>120 seconds The student who came first spent 120-105 = <<120-105=15>>15 seconds in the race #### 15 If Katherine has 4 apples and 3 times as many pears in her fridge, how many bananas does she have if she has a total of 21 pieces of fruit? Katherine has a total of 3 * 4 apples = <<3*4=12>>12 pears She therefore had 4 apples + 12 pears = <<4+12=16>>16 apples and pears We know she has 21 total pieces of fruit, so this means she must have 21 total - 16 = <<21-16=5>>5 bananas #### 5 Peter is raking leaves. It takes him 15 minutes to rake 3 bags of leaves. If he keeps raking at the same rate, how long will it take him to rake 8 bags? We are trying to figure out how long it will take Peter to rake 8 bags of leaves, so we'll call that Y. And we know Peter can rake 3 bags of leaves / 15 minutes = 8 bags of leaves / Y. Next, we will multiply to find the cross-products. 3 x Y = 15 x 8 or 3Y = 120. We want to get figure out Y, so we need to get it by itself by dividing by 3, like this: 3Y/3 = 120/3 or Y = 40 minutes. #### 40 Lovely cuts her birthday cake into 12 equal pieces. Only one-fourth of the cake was eaten by her visitors and the rest were kept. How many slices of cake were kept? 12/4 = <<12/4=3>>3 slices of cake were eaten by Lovely's visitors. So, 12 - 3 = <<12-3=9>>9 slices of cake were kept. #### 9 Jacoby wants to save money for a trip to Brickville. He needs to have $5000 total to go on his trip. He works a job earning $20 per hour and works 10 hours. He then finds he can sell cookies for $4 each, and he sells 24 pieces of cookies. With the money he has so far, he buys a lottery ticket for $10 and wins $500. Finally, he gets $500 from both of his sisters as a gift. How much more, in dollars, does Jacob need to go to Brickville? Jacob earns $20 per hour * 10 hours = $<<20*10=200>>200 for working. So he earns $4 each * 24 = $<<4*24=96>>96 for the cookies. So far he has earned $200 + $96 = $<<200+96=296>>296. He buys a lottery ticket so $296 - $10 = $<<296-10=286>>286 was left in his money. After winning in a lottery, he had a total of $500 + $286 = $<<500+286=786>>786. He gets $500 * 2 per sister = $<<500*2=1000>>1000 from her sisters. So he has so far $1000 + $786 = $<<1000+786=1786>>1786. He needs $5000 - $1786 = $<<5000-1786=3214>>3214. #### 3214 Sam bought a dozen boxes, each with 30 highlighter pens inside, for $10 each box. He rearranged five of these boxes into packages of six highlighters each and sold them for $3 per package. He sold the rest of the highlighters separately at the rate of three pens for $2. How much profit did he make in total, in dollars? Sam bought 12 boxes x $10 = $<<12*10=120>>120 worth of highlighters. He bought 12 * 30 = <<12*30=360>>360 highlighters in total. Sam then took 5 boxes × 6 highlighters/box = <<5*6=30>>30 highlighters. He sold these boxes for 5 * $3 = $<<5*3=15>>15 After selling these 5 boxes there were 360 - 30 = <<360-30=330>>330 highlighters remaining. These form 330 / 3 = <<330/3=110>>110 groups of three pens. He sold each of these groups for $2 each, so made 110 * 2 = $<<110*2=220>>220 from them. In total, then, he earned $220 + $15 = $<<220+15=235>>235. Since his original cost was $120, he earned $235 - $120 = $<<235-120=115>>115 in profit. #### 115 John starts at an elevation of 400 feet. He travels downward at a rate of 10 feet down per minute for 5 minutes. What is his elevation now? He traveled down 10*5=<<10*5=50>>50 feet. So he is at an elevation of 400-50=<<400-50=350>>350 feet. #### 350 Mark plants some strawberries in his backyard. Every month, the number of strawberry plants doubles. After 3 months, Mark digs up 4 strawberry plants and gives them to his friend. If he still has 20 strawberry plants, how many did he initially plant? First, add the 4 plants Mark gave away to the 20 he has left: 4 + 20 = <<4+20=24>>24 Then divide this number by 2 to find how many plants Mark had after two months: 24 / 2 = <<24/2=12>>12 Then divide that number by 2 to find how many plants Mark had after one month: 12 / 2 = <<6=6>>6 Finally, divide that number by 2 to find out how many plants Mark initially planted: 6 / 2 = <<6/2=3>>3 #### 3 Tom opens an amusement park. It cost $100,000 to open initially. It also cost 1% of that to run per day. He sells 150 tickets a day for $10 each. How long will it take to make back his money? It cost 100,000*.01=$<<100000*.01=1000>>1,000 a day to keep the place open He makes 150*10=$<<150*10=1500>>1500 a day from the park So he makes a profit of 1500-1000=$<<1500-1000=500>>500 a day So it takes 100000/500=<<100000/500=200>>200 days to make back his money #### 200 Georgia is working on a math test with 75 problems on it. After 20 minutes she has completed 10 problems. After another 20 minutes, she has completed twice as many problems. She has 40 minutes to complete the rest of the test. How many problems does she have left to solve? Georgia's test started with 75 problems and then Georgia completed 10, 75 - 10 = <<75-10=65>>65 problems. After 20 minutes she completes twice as many problems, 10 x 2 = <<10*2=20>>20. With 40 minutes left she has completed 10 + 20 problems = <<10+20=30>>30 problems. From the original 75 problems she has solved 30, 75 - 30 = <<75-30=45>>45 problems she has left. #### 45