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Zorluk: OrtaCaselets and Paragraph-Based Data

A recent agricultural survey evaluated the annual yield of three crops—Wheat, Rice, and Maize—across two neighboring regions, Region Alpha and Region Beta. The combined yield of all three crops in both regions was 8,0008,000 metric tons. Region Alpha accounted for 55%55\% of the total combined yield. In Region Alpha, the yield of Maize was 800800 metric tons, and the remaining yield was distributed between Wheat and Rice in the ratio of 5:45:4, respectively. In Region Beta, the yield of Rice was exactly half of the Wheat yield in Region Alpha. Additionally, the Maize yield in Region Beta was 20%20\% higher than the Maize yield in Region Alpha.

Based on the survey data, what is the ratio of the Wheat yield in Region Beta to the total Maize yield from both regions combined?

  1. A
    41:2441:24
  2. B
    44:4144:41
  3. 41:4441:44Cevap
  4. D
    47:3847:38

Cevap

The ratio of the Wheat yield in Region Beta to the total Maize yield from both regions is 41:4441:44.
The correct ratio is determined by first finding the Wheat yield in Region Beta (1,6401,640 metric tons) and the total Maize yield from both regions combined (1,7601,760 metric tons). Simplifying the ratio 1,640:1,7601,640 : 1,760 by dividing both values by 4040 yields the final result of 41:4441:44.

Adım Adım Çözüm

1
Determine the total crop yield for each region.
Region Alpha total = 4,4004,400 tons; Region Beta total = 3,6003,600 tons.
Region Alpha is 55%55\% of the 8,0008,000 total (0.55×8000=44000.55 \times 8000 = 4400). Region Beta is the remainder (8000−4400=36008000 - 4400 = 3600).
2
Calculate the individual crop yields for Region Alpha.
Maize = 800800 tons, Wheat = 2,0002,000 tons, Rice = 1,6001,600 tons.
Maize is given as 800800. The remainder for Wheat and Rice is 4,400−800=3,6004,400 - 800 = 3,600. Using the 5:45:4 ratio, Wheat is 59×3600=2000\frac{5}{9} \times 3600 = 2000, and Rice is 49×3600=1600\frac{4}{9} \times 3600 = 1600.
3
Calculate the individual crop yields for Region Beta.
Rice = 1,0001,000 tons, Maize = 960960 tons, Wheat = 1,6401,640 tons.
Rice is half of Region Alpha's Wheat (0.5×2000=10000.5 \times 2000 = 1000). Maize is 20%20\% higher than Region Alpha's Maize (800+0.20×800=960800 + 0.20 \times 800 = 960). Wheat is the remainder of Region Beta's total (3600−1000−960=16403600 - 1000 - 960 = 1640).
4
Calculate the required ratio.
The final ratio is 41:4441:44.
Total Maize from both regions is 800+960=1,760800 + 960 = 1,760. The ratio of Region Beta's Wheat to Total Maize is 1640:17601640 : 1760, which simplifies to 164:176164 : 176, and further to 41:4441 : 44 by dividing both numbers by 44.

Anahtar Kavram

Extracting interrelated data points from a narrative caselet to compute multi-step ratios and percentages.
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Konular

Caselets and Paragraph-Based Data

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