Final answer:
Grace's message costs were calculated by adding the initial fixed cost for the first 12 words to the variable cost of the remaining 48 words at a specific rate per word. However, the final calculated amount does not match the given options, indicating a potential error.
Step-by-step explanation:
The question involves calculating the total cost of sending a message based on a given pricing scheme. Grace sent a 60-word message, with the first 12 words costing 40k and each additional word costing 2k. To find the total amount Grace paid, we calculate the cost of the first 12 words and then add the cost for the remaining 48 words.
The fixed cost for the first 12 words is 40k. There are 60 - 12 = 48 extra words. The extra cost is 48 words × 2k per word = 96k. The total cost is the fixed cost plus the extra cost which is 40k + 96k = 136k. However, since this option is not available in the provided choices, there must be a mistake in understanding the question or the calculation.