Antonio and abby had the same number of paperclips. after antonio gave 30 paperclips to abby. abby had twice as many paperclips as antonio. how many paperclips did they have in all?
(draw before and after model. start with 3 units each)

180 paperclips.

Step-by-step explanation:

Let be "x" the number of paperclips Antonio had and "y" the number of paperclips Abby had.

We know that Antonio and Abby had the same number of paperclips. This can be expressed as:

After Antonio gave 30 paperclips to Abby, she had twice as many paperclips as Antonio. This is:

Substitute the first equation  into the second equation and solve for "y":

Since both had the same number of paperclips, we must multiply the value obtained by 2 in order to find the number paperclips they had in all.

Then:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

b