Examkin

Question

Difficulty: MediumDividing in a Ratio

A supply sergeant is distributing 560560 pairs of cold-weather boots between two infantry companies (Company Alpha and Company Bravo) in a ratio of 3:43:4. How many MORE pairs of boots does Company Bravo receive than Company Alpha?

  1. A
    140
  2. 80Answer
  3. C
    280
  4. D
    320

Answer

80
The correct approach is to first find the total number of parts in the ratio (3+4=73 + 4 = 7). Dividing the total 560560 boots by 77 reveals that each part represents 8080 boots. Since Company Bravo has 44 parts and Company Alpha has 33 parts, the difference is exactly 11 part, which equals 8080 boots.

Step-by-Step Solution

1
Calculate the total number of ratio parts.
3+4=73 + 4 = 7 total parts
To distribute the total amount according to the ratio, you first need to know how many equal parts the total is being divided into.
2
Determine the value of a single part.
560÷7=80560 \div 7 = 80 boots per part
Dividing the total number of boots by the total number of ratio parts gives the value of one equal share.
3
Find the difference in ratio parts between the two companies.
4−3=14 - 3 = 1 part difference
Instead of calculating both companies' totals and subtracting, it is more efficient to find the difference in their ratio shares directly.
4
Calculate the difference in the number of boots.
1×80=801 \times 80 = 80 boots
Multiplying the difference in parts by the value of one part gives the exact difference in the final item count.

Key Concept

Dividing a quantity in a given ratio involves finding the total number of parts, the value of one part, and then applying that unit value to answer the specific question asked.

Alternative Method

You can calculate each company's share individually first: Company Alpha receives 3×80=2403 \times 80 = 240 boots. Company Bravo receives 4×80=3204 \times 80 = 320 boots. Then, subtract the smaller share from the larger share: 320−240=80320 - 240 = 80 boots.
Estimated Time:1m 0s
Rate this question

Topics

Dividing in a Ratio

More questions from this topic