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Zorluk: OrtaRatios, Rates, and Proportions

In a wildlife sanctuary habitat, the ratio of finches to sparrows is 3:53 : 5, and the ratio of sparrows to thrushes is 2:32 : 3. If there are 4545 thrushes in the habitat, what is the total number of finches, sparrows, and thrushes?

  1. A
    48
  2. 93Cevap
  3. C
    102
  4. D
    125
  5. E
    165

Cevap

The total number of birds in the habitat is 93.
To find the total number of birds, first combine the finch-to-sparrow ratio (3:53 : 5) and the sparrow-to-thrush ratio (2:32 : 3) into a single three-part ratio. Since sparrows are common to both, scale the ratios so that sparrows have the same number of parts: 3:5=6:103 : 5 = 6 : 10 and 2:3=10:152 : 3 = 10 : 15. The combined ratio of finches to sparrows to thrushes is 6:10:156 : 10 : 15. Since there are 4545 thrushes corresponding to 1515 parts, 11 part represents 45÷15=345 \div 15 = 3 birds. The total number of parts is 6+10+15=316 + 10 + 15 = 31, so the total number of birds is 31×3=9331 \times 3 = 93.

Adım Adım Çözüm

1
Unify the two given ratios using a common term for sparrows.
The ratio of finches to sparrows is 3:5=6:103 : 5 = 6 : 10. The ratio of sparrows to thrushes is 2:3=10:152 : 3 = 10 : 15. Combined ratio of finches to sparrows to thrushes is 6:10:156 : 10 : 15.
Since sparrows appear in both ratios with values 55 and 22, finding the least common multiple (1010) allows all three quantities to be expressed in a single triple ratio.
2
Determine the value of one ratio unit using the known quantity of thrushes.
Thrushes correspond to 1515 ratio parts. Value per unit =4515=3= \frac{45}{15} = 3 birds.
Given that there are 4545 thrushes and they represent 1515 units in the combined ratio, dividing the total thrushes by 1515 gives the multiplier for each unit.
3
Calculate the total number of birds across all three species.
Total ratio units =6+10+15=31= 6 + 10 + 15 = 31 units. Total birds =31×3=93= 31 \times 3 = 93.
Multiplying the total number of ratio units by the value of a single unit yields the overall population of birds in the habitat.

Anahtar Kavram

Combining Compound Ratios and Scaling Proportions
Tahmini Süre:1m 30s
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Konular

Ratios, Rates, and Proportions

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