2005 CEMC Gauss (Grade 7) Problems/Problem 22
Contents
Problem
In a bin at the Gauss Grocery, the ratio of the number of apples to the number of oranges is , and the ratio of the number of oranges to the number of lemons is . What is the ratio of the number of apples to the number of lemons?
Solution 1
We start by assuming that there are oranges. (We pick since the ratio of apples to oranges is and the ratio of oranges to lemons is , so we pick a number of oranges which is divisible by and by . Note that we did not have to assume that there were oranges, but making this assumption makes the calculations much easier.) Since there are oranges and the ratio of the number of apples to the number of oranges is , then there are apples. Since there are oranges and the ratio of the number of oranges to the number of lemons is , then there are lemons. Therefore, the ratio of the number of apples to the number of lemons is . Thus, the answer is .
Solution 2
Let the number of apples be . Since the ratio of the number of apples to the number of oranges is , then the number of oranges is . Since the ratio of the number of oranges to the number of lemons is , then the number of lemons is . Since the number of apples is and the number of lemons is , then the ratio of the number of apples to the number of lemons is . Therefore, the answer is .
See Also
2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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CEMC Gauss (Grade 7) |