Final answer:
To calculate the total cost of a 175 gram dish at a restaurant with fixed and variable costs, find the variable cost rate per gram from the given information, calculate the additional variable cost for 175 grams, and add to the fixed cost. The total cost of a 175 gram dish is $70.
Step-by-step explanation:
The student is asking how to calculate the total cost of a dish in a restaurant that has both fixed and variable costs, with the variable costs depending on the weight of the dish. To find the cost of a 175 gram dish, we need to first determine the variable cost for that weight and then add it to the fixed cost.
We are given that a 50 gram dish has a variable cost of $10, and a 100 gram dish has a variable cost of $30. From these data points, we can find the rate of change in variable cost per increase in weight. The increase from 50 grams to 100 grams (50 gram increase) corresponds to a $20 increase in variable cost ($30 - $10), which means the variable cost increases by $0.40 per gram ($20 / 50 grams).
To find the variable cost for a 175 gram dish, we calculate the additional cost beyond the known 100 gram dish: 175 grams - 100 grams = 75 grams. Then we calculate the added variable cost: 75 grams × $0.40 per gram = $30, and add this to the variable cost of a 100 gram dish: $30 + $30 = $60. Lastly, we add the fixed cost of $10: $60 + $10 = $70. Therefore, the total cost of a 175 gram dish is $70.