carcinoGeneticist
Answered

You have 12 cups of granola and 8 1/2 cups of peanuts to make trail mix. What is the greatest number of full batches of trail mix you can make?
Trail Mix Recipe:
2 3/4 cups granola
1 1/3 cups peanuts

Please help and show how to solve..



Answer :

So for the granola, you divide 12 by 2.75 (2 3/4), and you get 4.36, but you can only make full batches, so its just 4. Then, for the Peanut, you divide 8.5 (8 1/2) by 1.3333 (1 1/3) and you get 6.4, so you round that to 6. But, you need the full recipe, so it can't be 6, because you only have enough granola for four batches. so the answer is four. Am I making any sense?

The correct answer is:


4 full batches.


Explanation:


To solve this, we need to see how many "servings" (the amount needed for the recipe) of granola and peanuts we have.


We have 12 cups of granola. We need 2 3/4 cups. We need to see how many 2 3/4 cup-sized "servings" there are in 12 cups. We do this by dividing:


12 ÷ 2 3/4


Write both of these as improper fractions:

12/1 ÷ 11/4


To divide fractions, flip the second one and multiply:

12/1 × 4/11 = 48/11 = 4 4/11


This means we have 4 full servings of granola.


We have 8 1/2 cups of peanuts. We need 1 1/3 cups. We need to see how many 1 1/3 cups-sized "servings" there are in 8 1/2 cups. We do this by dividing:


8 1/2 ÷ 1 1/3


We need to write both of these as improper fractions:

17/2 ÷ 4/3


To divide fractions, flip the second one and multiply:

17/2 × 3/4 = 51/8 = 6 3/8


We have 6 full servings of peanuts.


The greatest number of full batches we can make will be the smaller of the two full servings we have. We have 4 full servings of granola and 6 full servings of peanuts; we cannot make 6 full batches of trail mix, since we don't have enough granola. This means we can only make 4 full batches.