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Difficulty: MediumRatios, Rates, and Proportions

A food packaging company produces a trail mix containing almonds, cashews, and raisins. The ratio of the weight of almonds to the weight of cashews is 3:23:2, and the ratio of the weight of cashews to the weight of raisins is 5:45:4. If a batch of trail mix contains 360360 ounces of raisins, what is the total weight, in ounces, of the trail mix?

  1. A
    840840
  2. B
    1,1251,125
  3. C
    1,3851,385
  4. 1,4851,485Answer

Answer

1,485
To find the total weight of the trail mix, we determine the weights of cashews and almonds using the given ratios and the weight of raisins. The weight of cashews is calculated as 54×360=450\frac{5}{4} \times 360 = 450 ounces. Using the weight of cashews, the weight of almonds is calculated as 32×450=675\frac{3}{2} \times 450 = 675 ounces. Summing the weights of all three components yields 675+450+360=1,485675 + 450 + 360 = 1,485 ounces.

Step-by-Step Solution

1
Use the given ratio of cashews to raisins to find the weight of the cashews.
The weight of the cashews is 450450 ounces.
Since the ratio of the weight of cashews to raisins is 5:45:4, we set up the proportion cashews360=54\frac{\text{cashews}}{360} = \frac{5}{4}. Solving for cashews gives cashews=360×54=450\text{cashews} = 360 \times \frac{5}{4} = 450 ounces.
2
Use the ratio of almonds to cashews to find the weight of the almonds.
The weight of the almonds is 675675 ounces.
Since the ratio of the weight of almonds to cashews is 3:23:2, we set up the proportion almonds450=32\frac{\text{almonds}}{450} = \frac{3}{2}. Solving for almonds gives almonds=450×32=675\text{almonds} = 450 \times \frac{3}{2} = 675 ounces.
3
Sum the weights of all three ingredients to find the total weight of the trail mix.
The total weight is 1,4851,485 ounces.
The total weight is the sum of the weights of almonds, cashews, and raisins: 675+450+360=1,485675 + 450 + 360 = 1,485 ounces.

Key Concept

Solving multi-step ratio problems by linking parts using a common element to find the total quantity.
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Topics

Ratios, Rates, and Proportions

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