At a school book sale, Noah bought eight books for 88 dollars and Charlotte bought nine books for 27 dollars. Are these rates proportional?
Before beginning this problem, Noah bought eight books and Charlotte bought only one more book than that. So she bought more books than Noah. Yet she spent less money. So our gut would be these are probably not proportional. But let’s go ahead and check.
First of all, how will we find these rates? A rate in this example will be found by taking the cost of the books and dividing by the number of books.
So Noah’s rate would be 88 dollars divided by the eight books, which is 11. So he spent a rate of 11 dollars per book. For Charlotte’s rate, she spent 27 dollars on nine books. That’s three dollars per book. She must be the bargain shopper.
So for these rates to be proportional, our fractions must equal the same rate. However, they do not simplify to be the exact same number. One was 11 and the other was three. Therefore, our final answer will be no. These rates are not proportional.