Examkin

Soru

Zorluk: OrtaRatios, Rates, and Proportions

A certain paint mixture requires green, yellow, and white paint in the ratio 2:3:52:3:5, respectively. A painter wants to create a lighter shade of this paint by doubling the amount of white paint used while keeping the amounts of green and yellow paint the same. If the painter wants to prepare a total of 3030 gallons of this new lighter paint mixture, how many gallons of white paint will be needed?

  1. A
    10
  2. B
    12
  3. C
    15
  4. 20Cevap
  5. E
    25

Cevap

20 gallons
The original ratio of green to yellow to white paint is 2:3:52:3:5. Since the amount of white paint is doubled while green and yellow remain the same, the new ratio of green to yellow to white is 2:3:102:3:10. The sum of the parts in the new ratio is 2+3+10=152 + 3 + 10 = 15 parts. The fraction of the new mixture that is white paint is 1015\frac{10}{15}, which simplifies to 23\frac{2}{3}. To find the number of gallons of white paint in a 3030-gallon mixture, multiply the fraction by 3030: 23×30=20\frac{2}{3} \times 30 = 20 gallons.

Adım Adım Çözüm

1
Determine the new ratio of the paint mixture.
The new ratio of green to yellow to white paint is 2:3:102:3:10.
The original ratio is 2:3:52:3:5, and the painter doubles the white paint component (5×2=105 \times 2 = 10) while green and yellow remain unchanged.
2
Calculate the total parts in the new mixture.
Total parts = 2+3+10=152 + 3 + 10 = 15 parts.
To find the fraction of the mixture each component represents, we must sum the ratio parts.
3
Find the fraction of the mixture that is white paint and compute the required gallons for a 3030-gallon mixture.
Gallons of white paint = 2020 gallons.
White paint represents 1015=23\frac{10}{15} = \frac{2}{3} of the total mixture. Multiplying this fraction by the total volume of 3030 gallons gives 23×30=20\frac{2}{3} \times 30 = 20 gallons.

Anahtar Kavram

Solving multi-part ratio problems where one component is scaled.

Alternatif Yöntem

Instead of using fractions of the total, you can define a constant of proportionality xx. The new amounts of green, yellow, and white paint are 2x2x, 3x3x, and 10x10x gallons respectively. The total volume is 2x+3x+10x=302x + 3x + 10x = 30, which simplifies to 15x=3015x = 30, so x=2x = 2. The volume of white paint needed is 10x=10(2)=2010x = 10(2) = 20 gallons.
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Ratios, Rates, and Proportions

Bu konudan daha fazla soru