Examkin

Soru

Zorluk: OrtaRatios, Rates, and Proportions

A community theater company uses a combination of red, yellow, and blue light filters to create a specific lighting effect on stage. The ratio of the number of red filters to yellow filters is 4:34:3, and the ratio of the number of yellow filters to blue filters is 2:52:5. If the lighting setup uses a total of 5858 filters across these three colors, how many blue filters are used in the setup?

  1. A
    10
  2. B
    12
  3. C
    16
  4. D
    28
  5. 30Cevap

Cevap

30
To find the number of blue filters, we must write a single combined ratio for Red : Yellow : Blue. Since Red : Yellow = 4:34 : 3 and Yellow : Blue = 2:52 : 5, we convert both ratios so that Yellow has the same term. Multiples of 33 and 22 give a common value of 66. Scaling Red : Yellow by 22 gives 8:68 : 6, and scaling Yellow : Blue by 33 gives 6:156 : 15. Thus, Red : Yellow : Blue = 8:6:158 : 6 : 15. The total number of ratio units is 8+6+15=298 + 6 + 15 = 29. Each ratio unit represents 58÷29=258 \div 29 = 2 filters. Therefore, the number of blue filters is 15×2=3015 \times 2 = 30.

Adım Adım Çözüm

1
Find a common value for the yellow ratio component to combine the two ratios into a single three-part ratio.
The ratio of Red to Yellow is 4:3=8:64:3 = 8:6. The ratio of Yellow to Blue is 2:5=6:152:5 = 6:15. Therefore, Red : Yellow : Blue = 8:6:158 : 6 : 15.
Yellow is the shared quantity between both given ratios, so its ratio value must be equal in both expressions to combine them.
2
Calculate the total number of ratio parts and determine the value of one part.
Total parts = 8+6+15=298 + 6 + 15 = 29 parts. Value per part = 5829=2\frac{58}{29} = 2 filters per part.
Dividing the total filter quantity by the total number of parts yields the scale factor for the ratio.
3
Multiply the blue filter ratio parts by the value per part.
15 parts×2=3015 \text{ parts} \times 2 = 30 blue filters.
The question specifically asks for the total quantity of blue filters.

Anahtar Kavram

Three-Quantity Ratio Combination and Scaling
Bu soruyu puanla

Konular

Ratios, Rates, and Proportions

Bu konudan daha fazla soru