Which is more money: 50% of the sum of $150 and $50 or 1.5 times
the difference between $50 and $150 ?

50% of the sum of $150 and $50 is greater.

Step-by-step explanation:

We are asked to which of the given two quantities is greater.

Let us find 50% of the sum of $150 and $50 as:    

Now, we will find 1.5 times  the difference between $50 and $150 as:

Therefore, 50% of the sum of $150 and $50 is greater than 1.5 times  the difference between $50 and $150.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.