Ratios & Proportions: Combining Ratios with Different Multipliers - Equate the Common Member

In McDonald's farm, the ratio of the number of goats to the number of sheep is half the ratio of the number of cows to the number of goats in his farm. If the ratio of the number of goats to the number of sheep is $$1{:}3$$, then what is the ratio of the number of sheep to the number of cows in the farm?

Correct.

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Expand the first ratio by 3 to equate the common member—goats.

       Cows    :   Goats   :   Sheep

1st ratio                             ( 3    :    9 )

2nd  ratio       ( 2        :         3 )

The ratio of sheep to cows is therefore $$\color{blue}{9{:}2}$$.

Incorrect.

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Incorrect.

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Incorrect.

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Incorrect.

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$$9{:}2$$
$$3{:}2$$
$$2{:}3$$
$$6{:}1$$
$$1{:}6$$

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