(in general, easier problems come first; answer key forthcoming)
3.1) If a chocolate bar costs 10c (as mentioned in Roald Dahl’s 1964 book!), list four different ways (combinations of coins) to pay exactly 10c for the Wonka bar.
List all the coin combinations you could use to pay the exact price of two Wonka bars– one for Charlie and one for Grandpa Joe. How many ways did you find?
3.2) If there is no sales tax on the chocolate bars above, how many bars can Charlie buy if he finds a quarter on the street?
Will he get any change back? If so, how much?
If the money Charlie finds in the street is a dollar bill, how many 10c candy bars could he buy then?
3.3) If Charlie uses the dollar he finds to buy a 40c loaf of bread for his family, and two of the Wonka bars above, how much money will he have left to give his parents?
3.4) If eight squares of chocolate make up a Wonka bar, and Charlie eats two squares, what fraction of the bar did he eat?
3.5) Four of Charlie’s classmates pool their change to buy 3 Wonka bars. Since each bar is marked into 8-squares, how many squares will each child get to eat?
3.6) As Charlie walks home from school, he stops to stare through the locked gate of the Wonka factory at 3:23pm. If he spends five minutes talking to a strange poetry-spouting tinker, and then 40 minutes more staring at the factory windows for signs of the workers who never go in & never come out, what time will it be when Charlie starts for home again?
If Charlie reaches home at 4:54pm, how many minutes walk does he live from the factory? How many minutes walk from home to school?
3.7) If Veruca wears a mink coat that cost $345 total, and has three others like it at home, what is the total amount spent on mink coats?
3.8) If Augustus Gloop goes on an all-chocolate diet, and can eat only 1500 calories a day, how many 250-calories Wonka bars can he eat each day?
3.9) As Charlie takes the first Wonka bar from a display box of them on the store shelf, he can see that the box had five stacks of four bars. How many bars fill a display box?
If each display box arrives in a case containing five rows of five display boxes, how many Wonka bars are in a case?
If a store orders 15 cases, how many Wonka bars would that be?
3.10) If Mr. Salt’s nut factory has 120 employees, and each employee can shuck the wrappers off three Wonka bars per minute, how many bars will be unwrapped in an hour? How many bars would be unwrapped in an 8-hour work day?
About how many cases would that be?
3.11) If Mr. Beauregarde earns a 10% commission on the cars he sells, how much commission did he earn on the day he sold a $1200 car, a $1350 car, a $2600 car, and a $4500 station wagon?
If Mr. Beauregarde’s commission is 10% on the first $5000 worth, and 20% thereafter, what would he earn then?
3.12) [refers to #3.9 above] If Augustus Gloop eats 75% of a display box of Wonka bars, how many bars did he eat?
If he eats 15% of a case, how many Wonka bars would that be?
3.13) If a Wonka bar is 250 calories, what percentage of the daily 1500 calories would that one bar be?
3.14) [refers to #3.9 above] How many Wonka bars would make up 75% of a case?
What percentage of a case is 125 bars?
3.15) [refers to #3.9 above] Express the following as both a ratio, and a percentage:
If the store above receives a golden ticket somewhere in its shipment, and Charlie buys two Wonka bars, what chance does he have of finding it?
If one of the cases above has a golden ticket inside of it, and Charlie buys two Wonka bars, what are his chances of winning then?
If Charlie buys his two Wonka bars from the very display box that holds the golden ticket, what chance does he have of finding it?
3.16) An Oompa-Loompa has six candies in his pocket: a gobstopper, a caramel, a hair toffee, a luminous lolly, a rainbow drop, and a mint jujube. He decides to eat three and give three to his best friend. How many different combinations of candies could he eat?
3.17) One Scrumdiddlyumptious bar costs twice as much as a Nutty Crunch Surprise bar. If Mike Teavee spends $13.00 buying 10 Scrumdidlyumptious bars and 5 Nutty Crunch bars, what is the price of each Wonka bar?
3.18) Assume that Oompa-Loompas work for six days a week, and that they all work at the same rate. If a team of 3 Oompa-Loompas takes 3 weeks and 2 days to de-juice a giant blueberry, how long would it take a team of 4 Oompa-Loompas to do the same job?
3.19) The Oompa-Loompas pack 350 pounds of cavity-filling caramels into boxes that hold 1 ¾ pounds of caramel each. If each box sells for $1.75, what is the total selling price of all the caramel?
3.20) Every Everlasting Gobstopper weighs the same. The weight of a glass jar and the gobstoppers inside is 50 ounces. If the number of gobstoppers in the jar doubles, the total weight of jar and gobstoppers becomes 92 ounces. What is the weight of the jar?
3.21) A jar full of chocolate sauce weighs 10 pounds. When one-half of the sauce is poured out, the jar and remaining sauce weigh 5 ¾ pounds. How much does the jar weigh?
3.22) Draw a perfect square of chocolate, then divide it in half with a vertical line. Next draw two horizontal lines across the square to divide it into six congruent rectangles. If this square of chocolate has an area of 144 square inches, what is the perimeter of one of the rectangles?
3.23) Mr. Wonka has prepared a huge square of chocolate to send by Wonkavision. Draw the square, and draw two lines dividing the square into three congruent rectangles. If each of the three rectangles has a perimeter of 16 meters, how many meters are in the perimeter of the entire square?
3.24.) What is the volume of the Great Glass Elevator, if it is 81 inches deep, 55 inches wide, and 85 inches high? (The front, with door, is 55 in x 85in.) If Mr. Wonka decides to coat the entire exterior with chocolate sauce, what area needs to be covered?
If the floor and the door of the elevator do not have buttons, but every other square inch of the elevator contains a button, how many buttons total are inside?
3.25) Using the dimensions and weight of a contemporary Nestle Wonka bar, generate a reasonable estimate of the number of real Wonka bars you would need—and the pounds of chocolate that would be—to build Prince Pondicherry a chocolate palace. Assume each wall, floor, ceiling to be two bars thick, and provide the prince with a mimimum of 30 rooms, one of which must be over-sized like a ballroom or throne room. You may decide (and keep a list of) the room dimensions for yourself, and you may disregard doorways and windows. Once you have finished the problem, consider recalculating to allow for windows, deciding & listing the dimensions for yourself.
Author: Leigh Jerz
Webmaster: Dennis G. Jerz
17 Sep 2011 — math sections posted here