You draw a design for an art contest on a 3 inch by 5 inch card. the second phrase of the contest requires the drawing to be transferred to an 8.5 inch by 11 inches. standard sheet of paper and utilize as much of the space on the paper. type your exact answer in the blank without the units, and round to the nearest 10th

You probably meant:  "utilize as much of the space AS POSSIBLE on the paper."

Set up and solve an equation of ratios:

  3      8.5
=
  5        x

Then 3x = 42.5.  The image on the paper would be 8.5 by 42.5/3 inches, or 8.5 by 14.17 inches.  Won't fit!!

So, try this instead:

  3        x
=
  5       11

Then 5x =33, and x = 6.6.  An image with the same proportions as the 3x5 card will be 6.6 by 11 inches on the 8.5 by 11 inch paper.