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Zorluk: OrtaUS Customary Capacity and Volume

A groundskeeping crew is preparing a specialized liquid fertilizer. The instructions state to mix 44 fluid ounces of the concentrated fertilizer for every 33 quarts of water. If the crew uses 1212 gallons of water, how many cups of concentrated fertilizer must they add?

  1. A
    22
  2. 88Cevap
  3. C
    1616
  4. D
    6464

Cevap

The crew must add 88 cups of concentrated fertilizer.
The correct answer is found by first converting the 1212 gallons of water to quarts (12×4=4812 \times 4 = 48 quarts) so that it matches the ratio. Using the given rate, find the required concentrate: (48÷3)×4=64(48 \div 3) \times 4 = 64 fluid ounces. Finally, convert the fluid ounces to cups by dividing by the conversion factor (88 fluid ounces per cup), resulting in 88 cups.

Adım Adım Çözüm

1
Convert the total amount of water from gallons to quarts.
12 gallons×4 quarts/gallon=48 quarts12 \text{ gallons} \times 4 \text{ quarts/gallon} = 48 \text{ quarts}
The mixing ratio is given in terms of quarts, so the total water volume must match this unit before applying the proportion.
2
Calculate the total fluid ounces of concentrate needed for the water.
(48 quarts3 quarts)×4 fluid ounces=16×4=64 fluid ounces(\frac{48 \text{ quarts}}{3 \text{ quarts}}) \times 4 \text{ fluid ounces} = 16 \times 4 = 64 \text{ fluid ounces}
This scales the ratio up to the actual volume of water being used to find the total amount of concentrate required.
3
Convert the fluid ounces of concentrate into cups.
64 fluid ounces÷8 fluid ounces/cup=8 cups64 \text{ fluid ounces} \div 8 \text{ fluid ounces/cup} = 8 \text{ cups}
The question specifically asks for the final answer in cups, requiring a final conversion.

Anahtar Kavram

Multi-step volume conversions and proportional scaling
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US Customary Capacity and Volume

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