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Zorluk: Çok zorRatio, Proportion, and Percent Calculations

The table below displays quarterly logistics metrics for five regional distribution hubs of a global shipping enterprise in 2025:

HubTotal Units ShippedAir Freight Share (%)Q1 Avg Shipping Cost per Unit ($)Q4 Avg Shipping Cost per Unit ($)
North50,00030%120168
South60,00040%200260
East40,00025%150213
West75,00020%160192
Central30,00035%80108

For the hub that experienced the greatest percentage increase in average shipping cost per unit from Q1 to Q4, what is the ratio of its air freight unit volume to the non-air freight unit volume of the hub with the highest total overall expenditure in Q4?

  1. 5:185 : 18Cevap
  2. B
    1:61 : 6
  3. C
    5:125 : 12
  4. D
    10:910 : 9
  5. E
    2:32 : 3

Cevap

The ratio of the air freight unit volume of the hub with the greatest percentage cost increase (East) to the non-air freight unit volume of the hub with the highest Q4 expenditure (South) is 5 : 18.
East has the greatest percentage cost increase (42.0%42.0\%), yielding 10,00010,000 air freight units. South has the highest total Q4 expenditure ($15,600,000\$15,600,000), with a non-air freight unit volume of 36,00036,000. The simplified ratio of these two quantities is 10,000:36,000=5:1810,000 : 36,000 = 5 : 18.

Adım Adım Çözüm

1
Calculate the percentage increase in average shipping cost per unit from Q1 to Q4 for each hub.
North: 168−120120=40.0%\frac{168 - 120}{120} = 40.0\%
South: 260−200200=30.0%\frac{260 - 200}{200} = 30.0\%
East: 213−150150=42.0%\frac{213 - 150}{150} = 42.0\%
West: 192−160160=20.0%\frac{192 - 160}{160} = 20.0\%
Central: 108−8080=35.0%\frac{108 - 80}{80} = 35.0\%
Identify which hub achieved the greatest percentage increase in per-unit cost.
2
Identify the target hub and calculate its air freight unit volume.
The hub with the highest percentage increase is East (42.0%). Its air freight unit volume is 25%25\% of 40,000=10,00040,000 = 10,000 units.
Formulate the numerator for the final ratio.
3
Calculate total Q4 expenditure for each hub to find the hub with the highest overall expenditure.
North: 50,000×$168=$8,400,00050,000 \times \$168 = \$8,400,000
South: 60,000×$260=$15,600,00060,000 \times \$260 = \$15,600,000
East: 40,000×$213=$8,520,00040,000 \times \$213 = \$8,520,000
West: 75,000×$192=$14,400,00075,000 \times \$192 = \$14,400,000
Central: 30,000×$108=$3,240,00030,000 \times \$108 = \$3,240,000
The hub with the highest total Q4 expenditure is South ($15,600,000).
4
Calculate the non-air freight unit volume for South.
South non-air freight share =100%−40%=60%= 100\% - 40\% = 60\%. Non-air freight volume =60%= 60\% of 60,000=36,00060,000 = 36,000 units.
Formulate the denominator for the final ratio.
5
Compute and simplify the final ratio.
10,00036,000=1036=518\frac{10,000}{36,000} = \frac{10}{36} = \frac{5}{18} or 5:185 : 18.
Express the relationship in simplest integer ratio form.

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