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Difficulty: HardBasic Ratios

A defense contractor manufactures three types of vehicle armor panels: Type A, Type B, and Type C. The ratio of Type A panels to Type B panels produced is 2:32:3. The ratio of Type B panels to Type C panels produced is 4:54:5. If the contractor produces a total of 1,4001,400 panels across all three types, how many Type C panels are produced?

  1. A
    320
  2. B
    500
  3. 600Answer
  4. D
    1,000

Answer

600
To find the number of Type C panels, the two separate ratios must first be combined into one continuous ratio. Since Type B is in both ratios (33 parts in the first, 44 parts in the second), we find a common multiple, which is 1212. Scaling the ratios gives Type A : Type B = 8:128:12 and Type B : Type C = 12:1512:15. Combined, the ratio is 8:12:158:12:15. Adding these gives 3535 total parts. Dividing the 1,4001,400 total panels by 3535 reveals each part equals 4040 panels. Because Type C represents 1515 of those parts, we multiply 1515 by 4040 to get 600600 Type C panels.

Step-by-Step Solution

1
Identify the overlapping category (Type B) in both given ratios and find the least common multiple for its values (33 and 44).
The least common multiple of 33 and 44 is 1212.
To compare all three panel types simultaneously, they must be expressed within a single, unified ratio sequence.
2
Scale both original ratios so that Type B is represented by 1212 in both.
Multiply the first ratio (2:32:3) by 44 to get 8:128:12. Multiply the second ratio (4:54:5) by 33 to get 12:1512:15.
Multiplying both sides of a ratio by the same number keeps the proportions mathematically equivalent.
3
Combine the scaled ratios into a single three-part ratio and calculate the total number of parts.
The unified ratio of Type A to Type B to Type C is 8:12:158:12:15. The total number of parts is 8+12+15=358 + 12 + 15 = 35.
The total number of parts represents the entire production batch in ratio units.
4
Divide the total actual number of panels by the total ratio parts to find the value of one part, then calculate the total for Type C.
1,400÷35=401,400 \div 35 = 40 panels per part. Type C has 1515 parts, so 15×40=60015 \times 40 = 600 Type C panels.
This scales the ratio back up to the real-world quantities provided in the problem stem.

Key Concept

Combining Overlapping Ratios
Estimated Time:1m 30s
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Topics

Basic Ratios

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