Amy has a collection of X,Y, and Z's. Every X is a Y. One-half the Z's are Y's. There are 3 times as many Y's as X's. Amy has 50 Z's and 40X's.
No Z in an X.
How many Y's does Amy have that are neither X's nor Z's?
I found drawing a venn diagram helps solve this problem. There are 120 Ys, 40 XYs, and 25YZs. So, Ys only = 120-40-25 = 55
To find out how many Y's Amy has that are neither X's nor Z's, we need to analyze the given information step by step.
First, let's break down the information we have:
- Amy has 40 X's.
- Every X is a Y, which means all 40 X's are also Y's.
- One-half of the Z's are Y's. Amy has 50 Z's, so half of them would be 50/2 = 25 YZ's.
- There are 3 times as many Y's as X's. Since Amy has 40 X's, she has 3 * 40 = 120 Y's.
Now, let's use this information to find out how many Y's Amy has that are neither X's nor Z's:
- We know that Amy has a total of 120 Y's.
- Out of these, 40 are X's and 25 are YZ's.
- Therefore, the number of Y's that are neither X's nor Z's would be 120 - 40 - 25 = 55 Y's.
So Amy has 55 Y's that are neither X's nor Z's.