Final answer:
The correct calculation for the total amount of money, in terms of the variable X, is to use 25 cents per quarter and 5 cents per nickel. The total for (X + 2) quarters and 3X nickels is the sum of 25 times (X + 2) and 15 times X, which simplifies to 40X + 50 cents.
Step-by-step explanation:
The student is asking about how to find the total amount of money (in cents) when given a number of quarters and nickels, expressed in terms of a variable, X. Since quarters are worth 25 cents each and nickels are worth 5 cents each, the total amount of money can be calculated as follows:
- To find the value of X quarters, we multiply X by 25.
- To find the value of 3X nickels, we multiply 3X by 5.
Adding these amounts together yields the total amount of money in cents. Option 2 is the correct representation since it includes the stated number of coins: (X + 2) quarters, and 3X nickels. Therefore, the total amount of money is given by:
Total amount = (25 × (X + 2)) + (5 × 3X)
Which simplifies to:
Total amount = (25X + 50) + (15X)
Total amount = 25X + 15X + 50
Total amount = 40X + 50 cents