When Betty makes cheesecake, she sweetens it with a ratio of one part sugar to four parts cream cheese, and she flavors it with one teaspoon of vanilla for every two cups of cream cheese. For every one teaspoon of vanilla, she uses two eggs. She used two cups of sugar in her latest cheesecake. How many eggs did she use? Give the rationale and then the answer.
Let's think step by step. Betty used 2 cups of sugar in her cheesecake, so she used 2 * 1 = 2 times her ratio. Thus, she used 2 * 4 = 8 cups of cream cheese. She uses 1 teaspoon of vanilla for 2 cups of cream cheese, so she used 8 / 2 = 4 teaspoons of vanilla. For each teaspoon of vanilla, she uses 2 eggs, so she used 2 * 4 = 8 eggs.. The answer is: 8.

A loaf of bread was sliced into 15. Ten friends bought 4 loaves of bread. If they all eat all 4 loaves equally, how many slices of bread did each of them eat? Give the rationale and then the answer.
Let's think step by step. There are 15 x 4 = 60 slices of bread in 4 loaves of bread. Hence, each of them ate 60 / 10 = 6 slices of bread.. The answer is: 6.

Lilah's family gallery has 400 photos. On a two-day trip to the Grand Canyon, they took half as many photos they have in the family's gallery on the first day and 120 more photos than they took on the first day on the second day. If they added all these photos to the family gallery, calculate the total number of photos in the gallery. Give the rationale and then the answer.
Let's think step by step. On their first day to the grand canyon, the family took half as many photos as the ones they have in the gallery, meaning they took 1 / 2 * 400 = 200 photos. The total number of photos if they add the ones they took on the first day to the family's gallery is 400 + 200 = 600. On the second day, they took 120 more photos than they took on the first day, a total of 200 + 120 = 320 photos. After adding the photos they took on the second day to the galley, the number of photos will be 600 + 320 = 920.. The answer is: 920.