Lauren counted 27 students in the cafeteria the ratio of students that packed their lunch to those who bought lunch was 4:5 how many students bought their lunch

27 students is basically the sum of their ratios 4:5

We can define the proportion with an arbitary variable x - >

4x:5x

Which is the ratio of packed to bought lunch. Therefore, 4x + 5x = 9x. 9x = 27

x=3

The students that bought their lunch were the 5x group, therefore 15 students bought lunch.