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The ratio of apples to oranges in a bucket A is 1 to 3. Together, there are a total of 60 pieces of fruit in bucket A, which only includes apples and oranges. If you replace 5 apples from bucket A with 5 oranges from a different bucket, what is the new ratio of apples to oranges in bucket A?

Correct Answer:

**A**There initially are 15 apples and 45 oranges

- The first step here is to determine how many apples and oranges were in bucket A before the apples were switched with oranges. We know the ratio of apples to oranges was 1 to 3, and that, in total, there are 60 pieces of fruit. When dealing with ratios, it is often useful to use a little chart, such as this:

Ratio Multiplier Actual Apples Oranges Total - We can fill in the numbers we know--the ratio of apples to oranges is 1:3, meaning that the Total box under ratio is 4 (just add the apples to the oranges). We also know that the Actual Total is 60 pieces of fruit, so put the 60 in the Actual Total box.

Ratio Multiplier Actual Apples 1 Oranges 3 Total 4 60 - We can determine the multiplier by dividing 60 by 4, to get 15. The multiplier will always be the same for whatever you are comparing. So 15 goes in all three multiplier boxes. We can also fill in the Actual Apples box by multiplying 1 by 15, to get 15, and the actual oranges box by multiplying 3 by 15, to get 45.

Ratio Multiplier Actual Apples 1 15 15 Oranges 3 15 45 Total 4 15 60 - Now that we know that how many apples and oranges there were before the replacement of the apples, we can subtract 5 apples from 15 to get the number of apples there are now, which is 10. Further, we have to add 5 oranges, because we replaced the apples with oranges, so that we have 50 oranges. Therefore, the new ratio of apples to oranges is 10 : 50, which simplifies to 1:5, answer choice (A).