A bag contains colored marbles. The ratio of red marbles to blue marbles is 1 : 4. The ratio of blue marbles to yellow marbles is 2 : 5. What is the ratio of red marbles to yellow marbles?

c = 10

Step-by-step explanation:

Given that H varies directly as c³ then the equation relating them is

H = kc³ ← k is the constant of variation

To find k use the condition when H = 40, c = 2 , then

40 = k × 2³ = 8k ( divide both sides by 8 )

5 = k

H = 5c³ ← equation of variation

When H = 5 000, then

5000 = 5c³ ( divide both sides by 5 )

1000 = c³ ( take the cube root of both sides )

= c , so

c = 10