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Zorluk: OrtaDirect Proportions

An industrial cleaning solvent requires a mixture of Chemical A and Chemical B in a ratio of 5:25:2 by volume. If a worker uses 300300 milliliters of Chemical B, how many liters of the final cleaning solvent will be produced?

  1. A
    1050
  2. B
    0.75
  3. 1.05Cevap
  4. D
    10.5

Cevap

1.05
The correct answer accurately scales the mixture from parts to a total volume. Since the ratio of Chemical A to B is 5:2, there are 7 total parts in the mixture. Chemical B makes up 2 of these 7 parts. Setting up the proportion 2/7 = 300/x gives a total volume of 1050 mL. Converting this volume to liters by dividing by 1000 results in 1.05 liters.

Adım Adım Çözüm

1
Identify the ratio of Chemical B to the total mixture.
The mixture has 5 parts Chemical A and 2 parts Chemical B, making 7 total parts. The ratio of Chemical B to the total is 2:7.
To find the total volume based on the volume of one component, we need the part-to-whole relationship.
2
Set up and solve a proportion to find the total volume in milliliters.
2 / 7 = 300 / x. Cross-multiplying gives 2x = 2100, which simplifies to x = 1050 milliliters.
Direct proportions allow us to scale the ratio up to find the actual combined volume of the mixture.
3
Convert the total volume from milliliters to liters.
1050 / 1000 = 1.05 liters.
The question explicitly requires the final answer to be stated in liters.

Anahtar Kavram

Direct proportions and unit conversions in part-to-whole relationships

Alternatif Yöntem

Instead of setting up a formal proportion, use the unitary method. If 2 parts represent 300 mL, then 1 part equals 150 mL (300 / 2). The total mixture requires 7 parts, so the total volume is 7 * 150 = 1050 mL. Converting to liters gives 1.05 L.
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Direct Proportions

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