1. Riverside Middle School has 405 students. The ratio of girls to boys at t he school is 5:4. How many girls attend Riverside Middle School?
2. Three different numbers have a product of 36 and a sum of 11. What are the three numbers?
3. Farmer Dan wants to build a pen for his chickens to roam around. He has 24 feet of fencing. Assuming that he is going to build a rectangular pen and use natural-number lengths for the sides, what dimentions should he use to maximize the roaming are for the chickens?
4. Jamie is 3 times as old as her sister, Penny. In 2 years, Jamie will be twice as old as Penny. How old are Jamie and Penny now?
5. Imagine that on a coordinate plane you are only allowed to move along vertical and horizontal lines. The shortest distance between points, moving only vertically and horizontally, can be called the taxicab distance. What is the taxicab distance between the points (1, 3) and (6, -1)? Find a formula to calculate the taxicab distance between any two points A = (a,b) and B = (c,d).
10. If the sides of a square increase by 12 inches, the area increases by 200 square inches. What was the side length of the original square?
6. The vertices of a triangle are (1,1), (4,3) and (3,5). Find the area of the triangle.
7. Wilson, Dora, and Astra are different heights. What could be the order of their heights if exactly one of these statements is true and the others are false?
1. Wilson is the tallest.
2. Dora is not the tallest.
3. Astra is not the shortest.
9. Leo missed one of his first 4 free throws. What is the fewest number of consecutive free throws he must make to have a better than 90 percent free throw percentage?
8. An aquarium is in the shape of a rectangular prism that is 9 inches wide, 24 inches long, and 21 inches tall. The water in the aquarium is filled to a level that is 10 inches deep. Small metal cubes - each cube is 2 inches on a side - are place neatly in the aquarium, one at a time. How many cubes can you place in the aquarium before the water overflows?