Question

A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

• A. 82.2
• B. 92.2
• C. 101.2
• D. 110.4
• E. 165.6

Hint:

In ratio problems, first find the value of one "part" by using the known quantity. Once you know the value of one part, you can easily find the value of the total or any other component by multiplying.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a ratio problem. We are given the ratio of the parts of a mixture and the actual weight of one of the parts. We need to find the total weight of the mixture.
Step 2: Detailed Explanation:
The ratio of oats : raisins : nuts is 9 : 2 : 1.
This means that for every 9 parts of oats, there are 2 parts of raisins and 1 part of nuts.
The total number of "parts" in the ratio is the sum of the individual parts:
Total parts = \(9 + 2 + 1 = 12\) parts.
We are given that the weight of the nuts is 9.2 pounds. The nuts correspond to the "1" in the ratio.
So, 1 part of the mixture is equal to 9.2 pounds.
We need to find the weight of the total mixture, which is composed of 12 parts.
Total weight = (Total number of parts) \(\times\) (Weight per part)
\[ \text{Total weight} = 12 \times 9.2 \text{ pounds} \]
To calculate this:
\[ 12 \times 9 = 108 \]
\[ 12 \times 0.2 = 2.4 \]
\[ \text{Total weight} = 108 + 2.4 = 110.4 \text{ pounds} \]
Step 3: Final Answer:
The total mixture weighs 110.4 pounds.