In a farm, each cow eats twice as much grass as each sheep....

In a farm, each cow eats twice as much grass as each sheep. The cost of grass for 10 cows and 40 sheep for 20 days is $? 900$. Find the cost of grass for 20 cows and 10 sheep for 18 days (in ?).
(A) 600
(B) 675
(C) 750
(D) 800

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Key Concepts

Scaling Factors

Scaling factors are used when the problem involves changing the magnitude of variables, such as increasing or decreasing the number of animals or the duration in days. Recognizing the scaling relationship helps in directly computing the new cost or consumption from known values.

Unit Rates

Unit rates break down complex quantities into a per-unit measure (for example, cost per unit of grass or consumption per animal per day). This simplification is useful for scaling the computations to meet the requirements of different scenarios.

Ratios

Ratios compare the relative sizes of two quantities. In this type of problem, the ratio is used to compare the grass consumption of different animals (e.g., a cow eats twice as much as a sheep), allowing all consumptions to be expressed in terms of a common unit.

Proportional Reasoning

Proportional reasoning involves understanding that certain quantities, such as the amount of grass consumed or the total cost, change in direct proportion to factors like the number of animals or days. This concept is central to setting up relationships between given and unknown values in the problem.

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