If 10% of a number is 36 and 55% of the same number is 198, find 45% of that number.

9514 1404 393

  162

Step-by-step explanation:

There are many ways to work this. Perhaps the simplest is to recognize that 45% of the number is the difference between 55% of it and 10% of it.

  0.55n -0.10n = 0.45n

  198 -36 = 0.45n = 162

45% of the number is 162.

If you like, you can find the number as ...

  0.10n = 36

  n = 36/0.10 = 360

Then you can verify (if you like), that 55% of it is 198:

  0.55(360) = 198 . . . . true

Finally, you can figure 45% of it:

  0.45(360) = 162

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Using proportions, you can determine the number to be ...

  36/0.10 = n/0.45

  n = 0.45(36/0.10) = 4.5(36) = 162

"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.

3

step-by-step explanation: