Expert: Richard J. Raridon - 8/6/2006

Question
I can't seem to figure these out; however, I think I am headed in the right direction. Can you help me with these word problems?


1) Find two real numbers that differ by 5 and have a product of 16.

As I see this problem, the numbers do not have to be whole numbers, am I correct? Thus, this is what I came up with thus far: x-y=5, xy=16. Where do I go from here?


2)Dave's revenue SR on the sale of widgets is determined by the formula R=35x-x^2. His cost $C for producing x widgets is given by the formula C=5x+30. For what values of x is Dave's profit positive?

As I see it, Profit = Revenue - Cost
When you subtract the two equations, R and C, you get a quadratic, -x^2+30x-30. What values make this >0? Am I on the right track and can you help me solve this word problem? Please, I need to show all the work, this is the only way I will learn it.


3) A boxing ring is in the shape of a square, 33ft. on each side. How far apart are the fighters when one is in the center and the other in one of the corners?

As I see it, if I draw a square, put a dot in the center to represent the boxer in the center; Draw a line to one corner to represent the boxer in the corner. The sides are 33 in length, I should be able to use the pythagoean theory to solve this problem; however, I don't know how to set up the pythogorean in order to solve the problem. Can you help me figure this one out?


3) A taste test with 200 randomly selected people found that only three of them said that they would buy a box of new Sweet Wheat cereal. How many boxes could the manufacturer expect to sell in a country of 280 million people?

As I see it, (3/200)280,000,000 = 0.015 x 280,000,000 = 4.2 million boxes of cereal can be expected to be sold. Is this correct?


Thank you in advance for all of your help.

Cindy

Answer
1) You have two equations, two unknowns, so you can solve for x and y.  Since x = 5+y, you have (5+y)y = 16
or y^2+5y-16 = 0.  Solve for y
2) P = -x^2+30x-30 so you just put in values for x and calculate P.  P(1) = -1, P(2) = 26, etc.  The maximum value of P occurs at x=15.  Since it's a parabola, you need to find the value for x at which P is again negative.
3) Draw another line from the center to the middle of one of the sides nearest the boxer in the corner.  Now you have a right triangle with sides equal to 16.5.
3) 4.2 million is correct