Mark wants to build a pyramid of soda cases that's four levels tall. Each level of the pyramid has a square base where each side is one case longer than the level above it. The top level is just one case. How many cases of soda does Mark need? Give the rationale and then the answer.
Let's think step by step. We know that the top level just has one case. Since each level has one more case per side than the level above it, the second level has sides that are 2 cases long. We can figure out how many cases we need for the second level by finding the area of a square with a side length of 2: 2 cases * 2 cases = 4 cases. The third level has three cases per side, so we need to find the area of a square with side length 3: 3 cases * 3 cases = 9 cases. The fourth level has a side length of 4, so we find its area with 4 cases * 4 cases = 16 cases. Finally, we add up the number of cases we need on each level: 1 cases + 4 cases + 9 cases + 16 cases = 30 cases.. The answer is: 30.

A bicycle shop owner adds 3 bikes to her stock every week. After 1 month, she had sold 18 bikes but still had 45 bikes in stock. How many bikes did she have originally? Give the rationale and then the answer.
Let's think step by step. There are approximately 4 weeks in a month. The shop owner added 3 bikes every week for 4 weeks for a total addition of 3 * 4 = 12 bikes. The shop owner now has the original number of bikes + 12 bikes. She sold 18 bikes within the same time frame. She now has a total of 45 bikes which is: the original number of bikes + 12 - 18 = 45 bikes. The original number of bikes = 45 - 12 + 18 = 51 bikes.. The answer is: 51.

Carolyn counts 6 monkeys and 6 birds in the tree outside her window. Then two of the monkeys each eat one bird. What percent of the animals outside her window are monkeys now? Give the rationale and then the answer.
Let's think step by step. First find the new number of birds: 6 birds - 2 birds = 4 birds. Then find the new total number of animals: 6 monkeys + 4 birds = 10 animals. Then divide the number of monkeys by the number of animals and multiply by 100% to express the answer as a percentage: 6 monkeys / 10 animals * 100% = 60%.. The answer is: 60.