Jane bought pens for her three students. Each student received 62 red pens and 43 black pens. They pooled their pens together and took them from the pool whenever they needed them. After the first month, they had taken a total of 37 pens from the pool. After the second month, they had taken another 41 pens from the pool. Then Jane decided to split the remaining pens equally among them. How many pens will each student get now?

Each student got 62 + 43 =

<<62+43=105>>105 pens to start with. They pooled them to get 105 * 3 = <<105*3=315>>315 pens in the pool. They took 37 pens in the first month, leaving 315 - 37 = 278 pens in the pool. They took 41 pens in the second month, leaving 278 - 41 = 237 pens in the pool. 237 pens were split into three equal parts to give 237/3 = <<237/3=79>>79 pens each. #### 79 Hasan is packing up his apartment because he’s moving across the country for a new job. He needs to ship several boxes to his new home. The movers have asked that Hasan avoid putting more than a certain weight in pounds in any cardboard box. The moving company has helpfully provided Hasan with a digital scale that will alert him if a package is too heavy. Hasan is in the kitchen, and he fills a cardboard box with 38 dinner plates. When he checks the box, the scale reports his box is too heavy. Hasan knows each of his plates weighs 10 ounces. He removes a single plate from the box and checks the movers’ scale again. The scale reports his box is still too heavy. Hasan repeats the process again and again. When he has removed enough plates, the movers’ scale shows the box is now an acceptable weight for shipping. Hasan deduces that each shipping box can hold 20 pounds before the scale says the box is too heavy. How many plates did Hasan need to remove from the shipping box? Let x be the number of plates removed from the box. Hasan figured out the movers' weight limit was 20 pounds. Since a pound is equal to 16 ounces, each box can hold 20 * 16, or <<20*16=320>>320 ounces. Each plate weighs 10 ounces, so the weight of the plates in the box after Hasan removes enough plates to satisfy the movers' weight limit is (38 - x) * 10 ounces Since these two values are equal, we can write the equation (38 - x) * 10 = 320. Dividing both sides by 10 leaves 38-x = 32. Adding x to both sides gives 38 – x + x = 32 +x, or, 38 = 32 +x Subtracting 32 from both sides gives the value of x, which is the number of plates removed from the box, 38 -32 = 32 + x – 32, or, 6 = x #### 6 Nancy and Jason are learning to dance for the first time. Nancy steps on her partner's feet 3 times as often as Jason. If together they step on each other's feet 32 times, how many times does Jason step on his partner's feet? Let n be the number of times Nancy steps on her partner's feet and j be the number of times Jason does. We know that n = 3j and n + j = 32. Substituting the first equation into the second equation, we get 3j + j = 32 Combining like terms, we get 4j = 32 Dividing both sides by 4, we get j = 8 #### 8 Roberta started off with 8 vinyl records. Her friends gave her 12 records for her birthday and she bought 30 more at a garage sale. It takes her 2 days to listen to 1 record. How many days will it take her to listen to her record collection? She had 8 records, received 12 and bought 30 for a total of 8+12+30 = <<8+12+30=50>>50 records It takes 2 days to listen to 1 record and she has 50 records it will take her 2*50 = <<2*50=100>>100 days #### 100 On his farm, Mr. Mathews has goats and sheep in the ratio of 5:7. He decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. How much money does he make from the sale of the animals if the total number of sheep and goats on the farm is 360? The total ratio of goats and sheep on the farm is 5+7 = <<5+7=12>>12 The fraction that represents goats from the total ratio is 5/12, and since there are 360 goats and sheep on the farm, the number of goats is 5/12*360= <<5/12*360=150>>150 The number of sheep on Mr. Mathews's farm is 360-150 = <<360-150=210>>210. Mr. Mathews sold 1/2*150 = <<1/2*150=75>>75 goats. If each goat went for $40, the total amount of money Mr. Mathews made from the sale of his goats is 75*$40 = $<<75*40=3000>>3000 He also sold 2/3*210 = <<2/3*210=140>>140 of the total sheep on his farm. The income from the sale of the sheep is 140*$30=$<<140*30=4200>>4200 From the sale of goats and sheep, Mr. Mathews made $4200+$3000 = $8600 #### 7200 The average score on last week's Spanish test was 90. Marco scored 10% less than the average test score and Margaret received 5 more points than Marco. What score did Margaret receive on her test? The average test score was 90 and Marco scored 10% less so 90*.10 = <<90*.10=9>>9 points lower The average test score was 90 and Marco scored 9 points less so his test score was 90-9 = <<90-9=81>>81 Margret received 5 more points than Marco whose test score was 81 so she made 5+81 = <<5+81=86>>86 on her test #### 86 At the park, Dimitri saw families riding bicycles and tricycles. Bicycles have two wheels and tricycles have three wheels. 6 adults were riding bicycles and 15 children were riding tricycles. How many wheels did Dimitri see at the park? Dimitri saw 2 x 6 = <<2*6=12>>12 wheels on the bicycles. He saw 15 x 3 = <<15*3=45>>45 wheels on the tricycles. He saw a total of 12 + 45 = <<12+45=57>>57 wheels. #### 57 Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather? Of the 12 red mushrooms, 2/3 had spots, for a total of (2/3)*12=<<2/3*12=8>>8 white-spotted mushrooms. Of the 6 brown mushrooms, 100% had spots, for a total of (100/100)*6=<<6*100/100=6>>6 white-spotted mushrooms. Of the 14 green mushrooms, 0% had white spots, for a total of 14*0=<<14*0=0>>0 white-spotted mushrooms. And of the 6 blue mushrooms, half had spots, for a total of (1/2)*6=<<6*1/2=3>>3 white-spotted mushrooms. In total, they gathered 8+6+0+3=<<8+6+0+3=17>>17 white-spotted mushrooms. #### 17 Nicky went to the DMV. He spent 20 minutes waiting to take a number, and quadruple that amount of time plus 14 minutes waiting for his number to be called. How long did he wait total? First find how long Nicky spent waiting for his number to be called: 4 * 20 minutes + 14 minutes = <<4*20+14=94>>94 minutes Then add the time he spent waiting to take a number: 94 + 20 = <<94+20=114>>114 minutes #### 114 In my school, the number of students has increased by 20% this year. The number of students this year is 960. How many students were there last year? Let X be the number of students last year. The number of students this year is X+X*20% = 960 Combining like terms, we get X*1.2 = 960 Dividing both sides by 1.2, we get X = 800 students. #### 800