The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

Next, note the change in *ratio* in the apples column:
| | O | | A | |
|----------------|---|---|----|-----------|
| Original ratio | 3 | : | 4 | |
| Change | | | –2 | –4 apples |
| New ratio | 3 | : | 2 | |
Use the difference in *ratio* units and the corresponding change in *real* to find the multiplier.
Since a decrease of 2 in the apples *ratio* (from 4 to 2) corresponds
to a decrease of 4 actual apples, the multiplier is simply $$\frac{4}{2} = \color{red}{2}$$.
Use the multiplier to find the required quantity. Remember to use the ratios in their expanded/reduced form, rather than the original form.
The question asks for the number of oranges, which is simply the original *ratio* of $$3 \cdot \color{red}{2} = \color{purple}{6}$$.

Incorrect.
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This is the multiplier, not the actual number of oranges.

Incorrect.
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This is the number of oranges in the ratio, not the actual number of oranges.

Incorrect.
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Carefully check your work.

Incorrect.
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You might have gotten this answer if you calculated the number of fruits in the basket, instead of the number of oranges.

Correct.
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Compare the two ratios—expand/reduce so that the unchanged quantity is represented by the same number in *ratio*. Note the change in ratio units.
The common quantity in those ratios is the unchanged number of oranges. The ratio units of the oranges are already equal, so the ratios may be combined as is—no need to reduce/expand the ratios in order to compare them.

2

3

6

9

10

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