Solution for the maximum value, Problem for free throws
Thanks everyone for trying out the problem and posting in the comments! I'll try to put up a little easier problem this time.
Suppose that |x + y| + |x - y| = 2. What is the maximum possible value of x^2 - 6x + y^2?
When you first look at x^2 - 6x + y^2 you'll realize that if you want the maximum value, x would have to be a negative number to cancel out the -6x. Also, for the equation to be the maximum value, x and y would have to be the greatest absolute value possible.
From the equation |x + y| + |x - y| = 2, you can see that |x + y| and |x - y| has to be less than 2. Basically, from looking at the problem for a bit, you can see that if x=-1 and y=1 the equation works.
|x + y| + |x - y| = 2
|-1 + 1| + |-1 - 1| = 2
|0| + |-2| = 2
|-2| = 2
2 = 2
If you plug in -1 for x and 1 for y into x^2 - 6x + y^2 you get 8 which is the answer.
The players on a basketball team made some three-point shots, some two-points shots, and some one-point free throws. They scored as may points with two-points shots as with three-points shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was 61 points. How many free throws did they make?
Good luck! and remember calculators are not allowed. :)