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Problem Solving #4

Question #1: While competing in a marathon event, John is behind Mike by 100 yards. John runs (x - 2) yards while Mike runs (x + 10) yards. What is the new distance between them?

Question #2: What is the sum of 10% of x and 20% of 2x?

Question #3: What are the solutions of the equation 5x(x + 1)·5x = 1?

Question #4: Out of all of the houses characterized in the table below, what is the percentage of new ranches?

 Houses Old New Total Ranch 23 ? 30 Colonial ? 40 ? Total 23 ? ?

Question #5: If one of the houses from the previous question is randomly selected, what is the probability that the selected house is a ranch?

 Houses Old New Total Ranch 23 7 30 Colonial 0 40 40 Total 23 47 70

Question #6: The AB side of the ABCD trapezoid is 4 and the BC side is 3. What is the area of the triangle ABD? Question #7: The side AB of the ABCD square is 10, AE = ED and BF = FC. What is the area of parallelogram BFDE? Question #8: The graphs of two lines, y = f(x) and y = g(x) are given below, and four regions, M, N, O, and P are also shown with different colors on the same graph. Which region is the solution set of the system of inequalities y < f(x) and y > g(x)?

Question #9: Find the value of x if:

x + y + z = 5
x + y - z = 3
x - y = 2

Question #10:What is 2% of 8%?