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Difficulty: MediumRatios, Rates, and Proportions

An automated manufacturing line produces component X and component Y in a ratio of 4:74:7. During a single production run, a total of 1,7601,760 components were produced. How many more component Y than component X were produced during this run?

  1. A
    160
  2. 480Answer
  3. C
    640
  4. D
    1,120
  5. E
    1,320

Answer

480 more component Y than component X were produced.
The total ratio parts equal 4+7=114 + 7 = 11. Dividing the total production of 1,7601,760 components by 1111 yields 160160 components per ratio part. Since component Y has 77 parts and component X has 44 parts, component Y has 7−4=37 - 4 = 3 more parts than component X. Multiplying 3×1603 \times 160 gives 480480, which is the exact additional amount of component Y produced.

Step-by-Step Solution

1
Find the total number of ratio parts
4+7=114 + 7 = 11 total parts
The ratio 4:74:7 indicates that for every 4 units of component X, there are 7 units of component Y, making up 11 equal parts of the total production.
2
Calculate the value of one ratio part
1,76011=160\frac{1,760}{11} = 160 components per part
Divide the total number of components produced by the total number of ratio parts.
3
Determine the difference in ratio parts between component Y and component X
7−4=37 - 4 = 3 parts
Subtract the ratio units of component X from component Y to find the difference in ratio parts.
4
Calculate the difference in actual components produced
3×160=4803 \times 160 = 480 components
Multiply the difference in ratio parts by the value of a single ratio part.

Key Concept

Solving Part-to-Part and Part-to-Whole Ratio Word Problems
Estimated Time:1m 0s
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Topics

Ratios, Rates, and Proportions

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