Final Answer:
The total amount earned by the bakery by selling the cakes during the holiday season is (b) $2,460.
Step-by-step explanation:
Let's break down the problem-solving process. The total number of cakes sold is 1,230. Now, we need to find out how many of each type of cake was sold. One-third of them are caramel cakes, which is 1/3 × 1230 = 410). One-half are chocolate cakes, which is (1/2 ×1230 = 615). The remaining cakes are banana cakes, so we can find this by subtracting the caramel and chocolate cakes from the total: (1230 - 410 - 615 = 205).
Now, we calculate the total amount earned. Let the cost of each caramel cake be $a, chocolate cake be $b, and banana cake be $c. The total earnings (E) can be expressed as (E = 410a + 615b + 205c). However, for simplicity, let's assume each type of cake costs the same (a = b = c). Therefore, (E = 1230a). Given that the total earnings are $2,460, we can set up the equation (1230a = 2460). Solving for (a), we get (a = 2).
Now, we can substitute this back into the total earnings equation: (E = 1230 × 2 = 2460). Therefore, the total amount earned by the bakery is $2,460, and the correct answer is (b) $2,460.
Therefore the correct option is b) $2,460