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Difficulty: EasyRatios, Rates, and Proportions

A bicycle factory produces road bikes and mountain bikes at a constant ratio of 22 to 33. If the factory produces 120120 road bikes in one day, how many mountain bikes does the factory produce in the same day?

  1. A
    80
  2. 180Answer
  3. C
    300
  4. D
    360

Answer

180
The ratio of road bikes to mountain bikes is 22 to 33. Since the factory produces 120120 road bikes, we can set up the proportion 23=120x\frac{2}{3} = \frac{120}{x}, where xx represents the number of mountain bikes. Solving for xx gives 2x=3602x = 360, which simplifies to x=180x = 180.

Step-by-Step Solution

1
Identify the given ratio and set up a proportion comparing road bikes to mountain bikes.
The ratio of road bikes to mountain bikes is 23\frac{2}{3}, so the proportion is Road BikesMountain Bikes=23\frac{\text{Road Bikes}}{\text{Mountain Bikes}} = \frac{2}{3}.
To find the unknown number of mountain bikes using the constant ratio.
2
Substitute 120120 for the number of road bikes and solve for the number of mountain bikes, xx.
120x=23  ⟹  2x=360  ⟹  x=180\frac{120}{x} = \frac{2}{3} \implies 2x = 360 \implies x = 180.
To calculate the exact number of mountain bikes produced.

Key Concept

Using ratios and proportions to solve word problems
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Topics

Ratios, Rates, and Proportions

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