Final answer:
David bakes 132 fruit cakes. After calculating the number of ginger and banana cakes from the total of 540 cakes, we subtract these to find the remaining number of orange and fruit cakes. We then use the ratio of orange to fruit cakes (3:4) to calculate exactly how many fruit cakes there are.
Step-by-step explanation:
To calculate the number of fruit cakes David bakes, we first need to determine the total number of cakes of each type based on the information given. David bakes 540 cakes in total. We know that 2/9 of the cakes are ginger cakes, and 35% of the cakes are banana cakes. To find the number of ginger cakes, we multiply 540 by 2/9:
Number of ginger cakes = 540 × (2/9) = 120 cakes
Similarly, for banana cakes, since 35% are banana, we calculate:
Number of banana cakes = 540 × 0.35 = 189 cakes
Now, we subtract the number of ginger and banana cakes from the total to find the number of orange and fruit cakes:
Number of orange and fruit cakes = 540 - (120 + 189) = 540 - 309 = 231 cakes
The ratio of the number of orange cakes to fruit cakes is given as 3:4. This ratio means that for every 3 orange cakes, there are 4 fruit cakes. To find out how many fruit cakes there are, we divide the total number of orange and fruit cakes (231) into 7 parts (since 3 parts will be orange cakes and 4 parts will be fruit cakes) and then multiply by 4 to find the number of fruit cakes:
Number of parts = 3 (orange) + 4 (fruit) = 7 parts
One part = 231 × (1/7) = 33 cakes
Number of fruit cakes = 33 × 4 = 132 cakes
Therefore, David bakes 132 fruit cakes.