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Difficulty: MediumRatios, Rates, and Proportions

A specialty beverage company creates a signature tea blend by combining Black Tea, Green Tea, and White Tea leaves in the ratio 5:3:25 : 3 : 2 by weight. A master blender prepares a batch of this signature blend that contains 1818 pounds more Black Tea leaves than Green Tea leaves. What is the total weight, in pounds, of this batch of signature tea blend?

  1. A
    36
  2. B
    45
  3. C
    60
  4. D
    72
  5. 90Answer

Answer

The total weight of the batch of signature tea blend is 90 pounds.
Let xx represent the weight in pounds of one ratio part. The weights of Black Tea, Green Tea, and White Tea are 5x5x, 3x3x, and 2x2x pounds, respectively. Since the batch has 1818 pounds more Black Tea than Green Tea, we set up the equation 5x−3x=185x - 3x = 18, which simplifies to 2x=182x = 18, giving x=9x = 9. The total ratio sum for the blend is 5+3+2=105 + 3 + 2 = 10 parts. Thus, the total weight of the batch is 10×9=9010 \times 9 = 90 pounds.

Step-by-Step Solution

1
Define the ratio quantities using a common variable x.
Black Tea weight = 5x5x, Green Tea weight = 3x3x, White Tea weight = 2x2x.
The given ratio of Black Tea to Green Tea to White Tea is 5:3:25 : 3 : 2.
2
Set up an equation based on the given difference between Black Tea and Green Tea.
5x−3x=18  ⟹  2x=18  ⟹  x=95x - 3x = 18 \implies 2x = 18 \implies x = 9.
The batch contains 18 pounds more Black Tea leaves than Green Tea leaves.
3
Calculate the total ratio parts and determine the total weight.
Total parts = 5+3+2=105 + 3 + 2 = 10. Total weight = 10x=10×9=9010x = 10 \times 9 = 90 pounds.
The total weight is the sum of all three tea leaf components.

Key Concept

Solving multi-part ratio word problems using a scaling multiplier based on part-to-part differences.
Estimated Time:1m 0s
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Topics

Ratios, Rates, and Proportions

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