Alice has a 4-inch by 5-inch photo of your school’s championship girls’ ice hockey team. To celebrate their recent
victory, your principal wants Alice to enlarge her photo for a display case near the main office. When Alice went to the print shop, she was confronted with many choices of sizes: 7-inch by 9-inch, 8-inch by 10- inch, and 12-inch by 16-inch.She’s afraid that if she picks the wrong size, part of the photo will be cut off. Which size should Alice pick and why?

In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.

We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.

Step 2:

The original photo was a 4-inch by 5-inch photo.

Option 1 is 7-inch by 9-inch, so the ratios are

[tex]\frac{7}{4} = 1.75, \frac{9}{5} = 1.8.[/tex] The ratios are different so this cannot be the enlarged photo's dimensions.

Option 2 is 8-inch by 10-inch, so the ratios are

[tex]\frac{8}{4} = 2, \frac{10}{5} = 2.[/tex] The ratios are the same so this can be the enlarged photo's dimensions.

Option 3 is 12-inch by 16-inch, so the ratios are

[tex]\frac{12}{4} = 3, \frac{16}{5} = 3.2.[/tex] The ratios are different so this cannot be the enlarged photo's dimensions.

So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.