Final answer:
Lina has Q = 12 - D quarters where D is the number of dimes. The total value of her quarters is 0.25 * (12 - D) dollars.
Step-by-step explanation:
The student wants to translate the following scenario into algebra: Lina has 12 coins in her purse. D of them are dimes and the rest are quarters. In order to find how many quarters Lina has, we'll set up an equation. Let's use the variable Q to represent the number of quarters. Since the total number of coins is 12, the equation is D + Q = 12. To find the number of quarters, we'll rearrange the equation to Q = 12 - D.
To determine how much money Lina has in quarters, we'll remember that each quarter is worth 25 cents. The total value of the quarters is 0.25 * Q. Substituting the previous expression for Q gives us Total value in quarters = 0.25 * (12 - D). This is the amount Lina has in quarters in dollars.
It's also worth noting that when converting between coin values and dollars, 100 pennies equal ONE dollar. This concept is often used when working with units of length, weight, and capacity as well.