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.