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?

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.