Question

2) Katie and Jacob are enlarging pictures in a school yearbook on the copy machine. The ratio of the width to the length of the enlarged photo will be the same as the ratio of the width to the length of the original photo. 25 points One of the photographs that they want to enlarge is a 3" x 4"photo. katie says that she can enlarge the photo to a 9" x 12", but Jacob disagrees. He says it will be 11" x 12". Who is correct? Explain your reasoning in words. * Enlarged Photo Original Photo 3 inches 4 inches

Answer 1

The original picture Katie and Jacob want to enlarge is 3 by 4 photographs

This means that the initial length of the photograph is 3 and the intial width of the photographs is 4

If both of them want to enlarge the photograph, then the scaling factor must be the same for both the width and length

Katie enlarge the photo to a 9 x 12

The ratio of the original photograph is 3 to 4

That is, 3 : 4

Katie enlarge the photo to a 9 x 12

Ratio of the enlarged photo by katie is 9 to 12

That is, 9 : 12

Equate the two ratio together

3/4 = 9/12

Introduce cross multiplication

We have,

3 x 12 = 4 x 9

36 = 36

Therefore, the ratio which katie enlarged the photo results to a proportion

For Jacob

Jacob enlarged the photo to 11 x 12

Equating the two ratios

3/4 = 11/12

3 x 12 = 4 x 11

36 = 44

This does not give us a proportion

Therefore, Katie is correct while Jacob is wrong