Question

1. practice nadeem has a photo that is 5 inches tall and 8 inches wide. he plans to print copies of the photo in different sizes. a. for one of the copies, nadeem enlarges the dimensions of the original photo by a factor of 3. what are the dimensions of the enlarged photo? b. for another copy, nadeem shrinks the dimensions of the original photo by a factor of 0.75. what are the dimensions of the smaller photo? c. nadeem has a 10 - inch - by - 10 inch photo album. he wants to make as large a copy of the original photo as possible to fit in the album. what are the largest dimensions the copy can be, if he keeps the proportion of the original photo? explain your answer.

Explanation:

Step1: Calculate enlarged height

Multiply original height by 3.
$5\times3 = 15$ inches

Step2: Calculate enlarged width

Multiply original width by 3.
$8\times3 = 24$ inches

Step1: Calculate shrunk height

Multiply original height by 0.75.
$5\times0.75 = 3.75$ inches

Step2: Calculate shrunk width

Multiply original width by 0.75.
$8\times0.75 = 6$ inches

Step1: Find the ratio of height - to - width of original photo

The ratio of the original photo is $\frac{5}{8}=0.625$.

Step2: Assume the width of the new photo is $x$ inches (to fit in the 10 - inch width of the album)

The height $h$ of the new photo, since the ratio is maintained, $h = 0.625x$. We want to fit it into a 10 - inch by 10 - inch album. If we set the width $x = 10$ inches, then the height $h=0.625\times10 = 6.25$ inches. If we set the height to 10 inches, then the width $w=\frac{10}{0.625}=16$ inches which won't fit. So the largest dimensions while maintaining proportion are based on using the width of the album as the limiting factor.

Answer:

Height: 15 inches, Width: 24 inches