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Difficulty: HardRatios and Proportions

An aviation mechanic is preparing 6060 liters of a de-icing fluid mixture. The current mixture has a ratio of pure chemical to water of 3:23:2. To meet severe weather regulations, the mechanic must alter the mixture so that the ratio of pure chemical to water is 4:14:1. Assuming no water is removed, how many liters of pure chemical must be added to the current mixture?

  1. A
    12
  2. 60Answer
  3. C
    96
  4. D
    204

Answer

60
The correct approach requires recognizing that the amount of water remains constant at 24 liters. To achieve a new ratio of 4 parts chemical to 1 part water, the final mixture must contain 4 times as much chemical as water (24×4=9624 \times 4 = 96 liters). Since there are already 36 liters of chemical in the mixture, you must add 96−36=6096 - 36 = 60 liters of pure chemical.

Step-by-Step Solution

1
Determine the total number of parts in the initial ratio.
3+2=53 + 2 = 5 total parts.
To find the volume of a single part, you must first know how many total parts make up the 60-liter mixture.
2
Calculate the initial volume of pure chemical and water.
60÷5=1260 \div 5 = 12 liters per part. Pure chemical = 3×12=363 \times 12 = 36 liters. Water = 2×12=242 \times 12 = 24 liters.
Finding the absolute volumes allows you to establish the constant value (water) that will be used for the new proportion.
3
Set up a proportion for the new mixture using the constant water volume.
Let xx be the added chemical. The new ratio is 36+x24=41\frac{36 + x}{24} = \frac{4}{1}.
Since no water is removed, the water volume remains 24 liters. The new chemical amount must maintain a 4:1 relationship with this 24 liters.
4
Solve the proportion for xx.
36+x=24×4⇒36+x=96⇒x=6036 + x = 24 \times 4 \Rightarrow 36 + x = 96 \Rightarrow x = 60 liters.
Isolating xx provides the exact volume of pure chemical that needs to be added to reach the desired target ratio.

Key Concept

Multi-step proportion scaling with a constant part and a changing total.
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Topics

Ratios and Proportions

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