Augmented Matrices and The Gauss-Jordan Method
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Problem #1: An isosceles triangle has legs that are each x inches long and a base that is y inches long. The perimeter of this triangle is 38 inches. The base is 8 inches shorter than the length of a leg. Find the length of each of the three sides. (Released TAK Fall 2005)
The length of the legs is 46/3 inches and the length of the base is 22/3 inches. Problem #2: A toy store set up some bargain tables in the shopping mall. Three children, Ali, Bob, and Cindy, bought some items. On the basis of the following information, determine how many items each child purchased. The total number of items purchased was 5. Ali paid $1 for each item he purchased, Bob paid $2 each and Cindy paid $3 each. The total spend by all three children was $10. The toy store gave balloons when items were purchased. Ali got 2 balloons for each item he purchased; Bob and Cindy got 1 balloon for each item. The children received a total of 6 balloons. 
Ali bought one item, Bob bought three items, and Cindy bought one item. Problem #3: A theater has a seating capacity of 900 and charges $2 for children, $3 for students, and $4 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $2800. How many children attended the show? 
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