The math teacher would be happy if the class average test score was at least 85. There are 10 students in the class, 5 of which scored a 92 on the test and 4 of which scored an 80. What would the last student have to score to at least make the teacher happy?

How many students scored a 92? ** 5 students scored a combined total of 92 * 5 =

<<92*5=460>>460 How many additional students scored an 80? ** 4 additional students scored a combined total of 80 * 4 = <<80*4=320>>320 How many students scored a 92 or an 80? ** 9 students therefore scored a combined total of 460 + 320 = <<460+320=780>>780 What is the minimum average score for the class? ** We know the total combined score for 10 students must be at least 85 average * 10 students = <<85*10=850>>850 What is the minimum score for the last student? ** Therefore, the last student must score at least an 850 - 780 = <<850-780=70>>70 #### 70 Milo's parents tell him that he can win cash rewards for good grades. He will get $5 times the average grade he gets. He gets three 2s, four 3s, a 4, and a 5. How much cash does he get? How many points does Milo get? ** His total score is 27 because (3 x 2) + (4 x 3) + 4 + 5 = <<3*2+4*3+4+5=27>>27 How many grades does Milo get? ** His total number of grades is 9 because 3 + 4 +1 +1 = <<3+4+1+1=9>>9 How many points is Milo's average grade? ** His average grade is a 3 because 27 / 9 = <<27/9=3>>3 How much cash does Milo get? ** He earns $15 because 5 x 3 = <<5*3=15>>15 #### 15 Charley has a bag that contains 51 white beads and 90 black beads. He reaches in the bag and pulls out 1/6 of the black beads and a third of the white beads. How many beads in total did Charley pull out? How many black beads does Charley pull out? ** Charley pulled out 90/6 = <<90/6=15>>15 black beads. How many white beads does Charley pull out? ** Charley pulled out 51/3 = <<51/3=17>>17 white beads. How many beads in total did Charley pull out? ** Charley pulled out 15+17 = <<15+17=32>>32 beads in total. #### 32 There are 10 rows of 15 chairs set up for the award ceremony. The first row is reserved for the awardees while the second and third rows are for the administrators and teachers. The last two rows are then reserved for the parents and the rest of the rows are for the students. If only 4/5 of the seats reserved for the students are occupied, how many vacant seats from the students can be given to the parents? How many rows are not reserved for the students? ** There are 1 + 2 + 2 = <<1+2+2=5>>5 rows that are not reserved for the students. How many rows are reserved for the students? ** Hence, 10 - 5 = <<10-5=5>>5 rows are reserved for the students. How many seats are reserved for the students? ** That is equal to 5 x 15 = <<5*15=75>>75 seats. How many seats are occupied by the students? ** But only 75 x 4/5 = <<75*4/5=60>>60 seats are occupied by the students. How many seats can be given to the parents? ** Therefore, 75 - 60 = <<75-60=15>>15 seats can be given to the parents. #### 15 John eats 3 meals a day. Breakfast is 500 calories. His lunch contains 25% more calories than that. His dinner is twice as many calories as lunch. He also has 3 shakes that are each 300 calories. How many calories does he get in a day? How many more calories is lunch than breakfast? ** Lunch is 500 * .25 = <<500*.25=125>>125 more calories than breakfast How many calories is lunch? ** That means it is 500 + 125 = <<500+125=625>>625 calories How many calories is dinner? ** So dinner is 625 * 2 = <<625*2=1250>>1250 calories How many calories are the shakes? ** The shakes are 3 * 300 = <<3*300=900>>900 calories How many calories does John eat in a day? ** So in total he eats 500 + 625 + 1250 + 900 = <<500+625+1250+900=3275>>3275 calories #### 3275 Three-quarters of the oil from a 4000-liter tank (that was initially full) was poured into a 20000-liter capacity tanker that already had 3000 liters of oil. How many more liters of oil would be needed to make the large tanker half-full? How many liters of oil would be poured into the tanker? ** Three-quarters of oil from the initially full 4000-liter tank would be 4000*(3/4)= <<4000*3/4=3000>>3000 liters How many liters of oil are in the large tanker now? ** In addition to the 3000 liters that were already in the large tanker, there are 3000+3000 = <<3000+3000=6000>>6000 liters in it now. How many liters of oil would be needed to make the large tanker half-full? ** The tanker would be filled to half capacity by (1/2)*20000 = <<(1/2)*20000=10000>>10000 liters of oil How many liters of oil are left to reach half capacity? ** There are 10000-6000 = <<10000-6000=4000>>4000 liters left to reach half capacity. #### 4000 Amy is collecting candy for the car pool. She has 5 chocolate bars, 7 times as many M&Ms as chocolate bars, and 6 times as many marshmallows as M&Ms. Amy then arranges the candies into baskets. If she fills each basket with 10 candies, how many baskets will Amy fill? How many M&Ms does Amy have? ** Amy has 5*7=<<5*7=35>>35 M&Ms. How many marshmallows does Amy have? ** Amy has 35*6=<<35*6=210>>210 marshmallows. How many candies does Amy have? ** Amy has 5+35+210=<<5+35+210=250>>250 candies. How many baskets will Amy fill? ** She fills 250/10=<<250/10=25>>25 baskets. #### 25 Since Jason started investing, he has earned the same amount he invested twice over in 5 months. If Jason's investment currently is worth $90, how much has he been earning per month from his investment assuming he has been earning an equal amount of returns each month? How much money did Jason invest? ** Let's say Jason invested x amount of money. How much money has Jason earned since he started investing? ** Since Jason started investing, he has earned the same amount he invested twice over in 5 months, meaning he has earned x+2*x=$90 How much money has Jason earned since he started investing? ** This evaluates to 3x=$90 How much money did Jason invest? ** The total amount of money that Jason invested is x=$90/3 How much money did Jason invest? ** Jason invested x=$30 How much money has Jason earned from his investments? ** The total amount of money that Jason has earned from his investments is $90-$30=$<<90-30=60>>60 How much money has Jason earned from his investment each month? ** If he earned an equal amount of money from the investment in five months, his monthly returns is 60/5=$<<60/5=12>>12 #### 12 It will cost $60 to rent a sailboat and $80 per hour to rent a ski boat. Ken rented a sailboat while Aldrich rented a ski boat. How much more did it cost Aldrich to rent the ski boat than Ken to rent a sailboat for three hours a day in two days? How much did Ken pay to rent a sailboat? ** Ken paid $60 x 3 = $<<60*3=180>>180 to rent a sailboat for 3 hours in a day How much did Aldrich pay to rent a ski boat? ** Aldrich paid $80 x 3 = $<<80*3=240>>240 to rent a ski boat in 3 hours in a day. How much more did it cost Aldrich to rent the ski boat than Ken to rent a sailboat for three hours a day in two days? ** So Aldrich paid $240 - $180 = $<<240-180=60>>60 more to rent a ski boat than Ken to rent the sailboat each day. How much more did it cost Aldrich to rent the ski boat than Ken to rent a sailboat for three hours a day in two days? ** Therefore, it cost Aldrich $60 x 2 = $<<60*2=120>>120 more to rent a ski boat than Ken to rent the sailboat in two days. #### 120 George and Harry want to fill a pool with buckets. George can carry two buckets each round, and Harry can carry three buckets each round. If it takes 110 buckets to fill the pool, how many rounds will it take to fill the pool? How many buckets can George and Harry carry in each round? ** Each round 2+3=5 buckets will be filled. How many rounds will it take to fill the pool? ** It will take 110/5=<<110/5=22>>22 rounds. #### 22