Final answer:
The correct expression that represents the total amount in cents that Richard has given that he has q quarters and d dimes is 25q + 10d.
Step-by-step explanation:
The student has asked for the correct expression to represent the total amount in cents that Richard has in his pocket, given that he has q quarters and d dimes. To solve this, we need to understand the value of each coin in cents since the question asks for the total amount in cents.
A quarter is worth 25 cents, and a dime is worth 10 cents. Knowing this, we can represent the total value of the quarters as 25q because each quarter (q) is 25 cents. Similarly, the total value of the dimes is 10d because each dime (d) is 10 cents. Therefore, to find the total amount in cents, we add the total value of the quarters and dimes, which leads us to the expression 25q + 10d.
This calculation is akin to converting between units of length, weight, and capacity, where you multiply the number of units by their respective conversion factors to find a total in a common unit of measurement. In this case, the common unit is cents, and we're converting quarters and dimes into that unit.