A basket of fruit contains apples, oranges and bananas in the ratio \( 3: 2,5 \). (From this, the numbe of apples:oranges is \( 3: 2 \), and oranges :bananas \( 2: 5 \).) a If there are 8 oranges, how many: (i) apples (ii) bananas, are there? b If there are 10 bananas, how many apples and
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From the ratio of apples to oranges \(3:2\), if there are 8 oranges, we can set up a proportion to find the number of apples. Since the ratio tells us that for every 2 oranges, there are 3 apples, we can calculate: \[ \text{Number of apples} = \frac{3}{2} \times 8 = 12. \] Next, we need to find the number of bananas. From the oranges to bananas ratio \(2:5\), if there are 8 oranges, the number of bananas can be calculated similarly: \[ \text{Number of bananas} = \frac{5}{2} \times 8 = 20. \] Now, if there are 10 bananas, we will revisit the oranges to bananas ratio again. Since \(2:5\) means for every 5 bananas, there are 2 oranges, we find the number of oranges like so: \[ \text{Number of oranges} = \frac{2}{5} \times 10 = 4. \] Now, plugging back to find the number of apples with 4 oranges, the apples from the first ratio comes out to be: \[ \text{Number of apples} = \frac{3}{2} \times 4 = 6. \] So, the answers are: a(i) 12 apples, (ii) 20 bananas b) 6 apples and 4 oranges.
