Case Problem:
In my favorite shopping mall downtown there is a specialty shop that's bound to please anybody's sweet tooth. It's a candy store called Candylandia. In this store you can find just about any kind of candy your tastebuds would savor.
One favorite and traditional candy is the candy corn. Candylandia sells candy corn in three different-sized jars: small, medium, and large. The owner, who loves fairy tales too, calls them the Baby Bean jar, the Mama Bean jar, and the Papa Bean jar, respectively.
Strange as it may seem, each jar of a given size always contains the same number of candy corn as any other jar of that size.
One day, Mrs. Goldie Lochs brought her 9-year-old set of triplets, who had a big craving for candy corn, into the store. Each child (Allen, Bradley, and Charles) bought two different jars of candy corns, but none of the combinations were the same. At home, the children decided to count the number of corns that they had purchased.
Allen announced, avidly, "I have 157 candy corns!"
Bradley boasted boldly, "But I have 47 more than you do, so there!"
Charles chimed in, calmly, "Well, I have 112 less than you two guys have together, but I'm not complaining."
Using this unusual collection of information, please tell me how many candy corns are placed in each jar. Be careful to properly identify any variables you use. State your equations and describe in words how you solved the problem. Then give your equations and work them out for us.
Provide complete and step by step solution for the question and show calculations and use formulas.