8 apples and 17 bananas cost as much as 5 apples and 19 bananas. Find the ratio of the cost of 3 bananas and 2 apples?
Question
8 apples and 17 bananas cost as much as 5 apples and 19 bananas. Find the ratio of the cost of 3 bananas and 2 apples?
Solution
Sure, let's solve this step by step.
Step 1: From the given problem, we can form two equations. Let's assume the cost of an apple is 'a' and the cost of a banana is 'b'.
The equations are:
8a + 17b = 5a + 19b (This is from the given "8 apples and 17 bananas cost as much as 5 apples and 19 bananas")
Step 2: Rearrange the equation to find the relationship between 'a' and 'b'.
8a - 5a = 19b - 17b 3a = 2b
Step 3: We need to find the ratio of the cost of 3 bananas to 2 apples.
From the above equation, we know that 3a = 2b. So, the ratio of the cost of 3 bananas to 2 apples is the same as the ratio of 3a to 2b.
Step 4: Substitute 'a' from the equation 3a = 2b into the ratio.
The ratio of the cost of 3 bananas to 2 apples is 3a : 2b = 3*(2b/3) : 2b = 2b : 2b = 1 : 1
So, the ratio of the cost of 3 bananas to 2 apples is 1:1.
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