# Video: Pack 2 • Paper 2 • Question 10

Pack 2 • Paper 2 • Question 10

02:13

### Video Transcript

Lucy baked pizzas, pies, and pasta dishes for an event. The ratio of pizzas to pies that she made is three to two. The ratio of pizzas to pasta dishes that she made is five to four. Less than 75 people will attend the event. And she made exactly one dish per person. What is the largest number of people who could have pasta?

The ratio of pizza to pie is three to two. And the ratio of pizza to pasta is five to four. Let’s consider what each ratio has in common. In both ratios, we are looking at the ratio of pizza to some other item. This means then that we need to scale up our ratios so that the ratio of pizzas is the same in each grouping. Once we do this, we’ll be able to compare every item.

Let’s start by multiplying both of the ratios in the ratio of pizza to pies by five. Remember, these are equivalent ratios. As long as we multiply or divide both part by the same number, the ratios are the same. We want the ratio that corresponds to pizzas in this second set of ratios to be 15. We will therefore multiply both parts of this ratio by three. That gives us that the ratio of pizza to pasta is 15 to 12.

We can now compare each of the items. The ratio of pies to pizza to pasta dishes is 10 to 15 to 12. We are told that less than 75 people attended the event. And we want to find the largest number of people who could have had pasta.

Currently, the sum of our parts is 10 plus 15 plus 12, which is 37. In this case then, we can scale our ratio up further by multiplying everything by two. 20 plus 30 plus 24 is 74. So this is the largest number of total dishes made. The part of our ratio that represents pasta dishes made is 24. The largest number of people who could have pasta is 24.