Problem Set #3

In the diagram, the sum of the numbers in each quarter circle is the same. the value of x + y + z is
a. 75
b. 64
c. 54
d. 171
e. 300

So this question is asking what the three unknown numbers are.

To solve this question, you first need to know how much is in each quadrant. In quadrant a (12 o' clock to 3 o'clock), you have all the numbers. 13 + 17 + 45 is equal to 75. If all the quadrants are equal in value, we can find out what x, y, and z are.
In the second quadrant (3 o'clock to 6 o'clock), the numbers present are 19, 50, and x. In this quadrant,19 + 50 + x = 75. Now, using simple algebra, we can take the two numbers move them to the other side, and subtract them from 75, therefore resulting in x. 


19 + 50 + x = 75
75 - 50 - 19 = x
6 = x


In order to find y and z, we repeat this process with the other 2 remaining quadrants.


63 + 3 + y = 75
75 - 3 - 63 = y
9 = y


28 + 8 + z = 75
75 - 8 - 28 = z
39 = z


Now that we know the values of x, y, and z, we can add them together to get the answer to the equation which is 6 + 9 + 39 = 54. So now we know the answer is C.


I liked this equation because at first it looks difficult but if you try hard enough, it is actually really simple and straightforward. It was one of those questions you barely get but once you finish it its like, "YES!" I thought this question was kinda fun.


In the process of problem solving, I learned that it may seem hard at first but when you know what to do, it gets easier. I learned that math can be fun even though it doesn't sound like it.