At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional?

Question

HIX Tutor · Accepted Answer

undefined To see if the rates are proportional, we need to check if the cost per book is the same for both Michael and Darnell. Here are the steps:

1. **Find Michael's cost per book:**
   - Michael bought 3 books for $6.
   - Cost per book = Total cost ÷ Number of books
   - Cost per book = $6 ÷ 3 = $2 per book.

2. **Find Darnell's cost per book:**
   - Darnell bought 5 books for $10.
   - Cost per book = Total cost ÷ Number of books
   - Cost per book = $10 ÷ 5 = $2 per book.

3. **Compare the costs:**
   - Michael's cost per book = $2
   - Darnell's cost per book = $2

Since both costs per book are the same, the rates are proportional.

Noah Archer · Answer

Yes, they are proportional. Both Michael and Darnel, paid $2 per book.

#6/3 = 10/5# #2 = 2#

Luna Angel · Answer

undefined To determine if the rates at which Michael and Darnell bought books are proportional, we can compare the ratios of the number of books to the amount spent for each of them.

Michael's rate: $ \frac{3 \text{ books}}{\$6} = \frac{1 \text{ book}}{\$2} $

Darnell's rate: $ \frac{5 \text{ books}}{\$10} = \frac{1 \text{ book}}{\$2} $

Both rates simplify to $ \frac{1 \text{ book}}{\$2} $.

Since both rates simplify to the same value, $ \frac{1 \text{ book}}{\$2} $, they are indeed proportional. Therefore, Michael and Darnell bought books at proportional rates.