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Difficulty: MediumRatios, Rates, and Proportions

A municipal water treatment facility mixes three treatment chemicals—coagulant, disinfectant, and pH adjuster—in the ratio 3:5:43 : 5 : 4 by volume. If the facility uses 120120 gallons of pH adjuster during a single shift, what is the total volume, in gallons, of all three chemicals combined used during that shift?

  1. A
    240
  2. B
    300
  3. 360Answer
  4. D
    480
  5. E
    1,440

Answer

360 gallons
The ratio of coagulant to disinfectant to pH adjuster is 3:5:43 : 5 : 4, giving a total of 3+5+4=123 + 5 + 4 = 12 parts. Since 44 parts of pH adjuster equal 120120 gallons, each part corresponds to 1204=30\frac{120}{4} = 30 gallons. The total volume of all three chemicals combined is 12×30=36012 \times 30 = 360 gallons.

Step-by-Step Solution

1
Determine the total number of ratio parts.
The total ratio parts are 3+5+4=123 + 5 + 4 = 12 parts.
Summing the individual terms of the ratio gives the total parts representing the entire chemical mixture.
2
Calculate the volume of one ratio part.
One part =120 gallons4 parts=30 gallons per part= \frac{120\text{ gallons}}{4\text{ parts}} = 30\text{ gallons per part}.
The pH adjuster accounts for 4 parts of the ratio and equals 120 gallons, so dividing 120 by 4 yields the value of 1 part.
3
Calculate the total volume of all three chemicals.
Total volume =12 parts×30 gallons per part=360 gallons= 12\text{ parts} \times 30\text{ gallons per part} = 360\text{ gallons}.
Multiplying the volume of a single part by the total number of parts yields the total volume.

Key Concept

Part-to-Whole Ratios and Proportions
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Topics

Ratios, Rates, and Proportions

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