You want to draw an enlargement of a design that is painted on a 4 in. by 5 in. You will be drawing this design on a piece of paper that is 8 1/2 in. by 11 in. What are the dimensions of the largest complete enlargement you can make?

Question

You want to draw an enlargement of a design that is painted on a 4 in. by 5 in. You will be drawing this design on a piece of paper that is 8 1/2 in. by 11 in. What are the dimensions of the largest complete enlargement you can make?

A. 1 3/5 in by 10 5/8 in
B. 1 3/8 in by 3/5 in
C. 8 1/2 in by 4 3/8 in
D. 8 1/2 in by 10 5/8 in

I don't understand. I tried cross multiplying:

w/4 = 11/5
5w = 44
w = 8.8

But that answer converted to fractions is 8 4/5, so there's no point there.

8.5/4 = w/5
5(8.5) = 4w
425 = 4w
106.25 = w

... I don't need to convert that to fractions to know that's not right!

I really don't understand this question, and if anyone could give me the answer (if I have the answer, I can usually figure it out on my own, but if if you don't mind step-by-step that'd welcome!), I'd GREATLY appreciate it! :)

Answer 1

a 4x5 card does not have the same aspect ratio as the 8.5x11 paper

enlarging 4 to 8.5 is a scale of 2.125
enlarging 5 to 11 is a scale of 2.2

So, using the smaller scale, 4x5 enlarges to 8.5x10.625

or, 8 1/2 by 10 5/8

trying to enlarge it more will cause the width to exceed the paper size.

Answer 2

Really? How did you get that answer? @Steve

Answer 3

um, what in the above solution, did you not understand?

Answer 4

How did you get 8.5x10.625?

Answer 5

Wait! Oh my goodness, I'm sorry! I totally get it now! XD THANK YOU SO MUCH! ^.^ You are a lifesaver. :)

Answer 6

To find the dimensions of the largest complete enlargement you can make, we need to compare the ratios of the sides of the design and the paper.

First, let's calculate the scale factor of the enlargement. Divide the length of the paper by the length of the design:

8.5 in. ÷ 4 in. = 2.125

Now, divide the width of the paper by the width of the design:

11 in. ÷ 5 in. = 2.2

The scale factor is the larger of the two ratios, which in this case is 2.2. This means that each dimension of the enlargement will be multiplied by 2.2.

Next, multiply each dimension of the design by the scale factor to find the dimensions of the enlargement:

4 in. × 2.2 = 8.8 in. (rounded to one decimal place)
5 in. × 2.2 = 11 in.

Therefore, the dimensions of the largest complete enlargement you can make are approximately 8.8 in. by 11 in. which corresponds to answer choice D.