Question

Rebecca wanted to buy a book at the book store for $3.50, including tax. She reached into her wallet and pulled out a handful of coins, all dimes and quarters. Let d represent the number of dimes and q represent the number of quarters. Which expression below describes how many of each coin she would need to have in order to have at least $3.50? A. d + q < 3.5 B. 10q + 25d > 350 C. 10d + 25q > 350 D. 10d + 25q < 350

Answer 1

The correct expression for Rebecca to have at least $3.50 in dimes and quarters is 10d + 25q ≥ 350. Given the choices, the closest correct option is 10d + 25q > 350, which is Option C.

Step-by-step explanation:

The student's question involves determining the correct expression to represent the amount of money Rebecca needs in dimes and quarters to have at least $3.50. A dime is worth $0.10, and a quarter is worth $0.25. Therefore, if d represents the number of dimes and q represents the number of quarters Rebecca has, the total amount of money she has in terms of dimes and quarters can be expressed as 10d + 25q, where the values are in cents. To have at least $3.50, which is equivalent to 350 cents, the inequality 10d + 25q ≥ 350 must be satisfied. Therefore, the correct expression that represents Rebecca needing at least $3.50 is 10d + 25q ≥ 350. However, since the choices provided do not include an inequality with ≥ but rather '>', we would choose the closest option, which assumes that Rebecca needs more than $3.50: 10d + 25q > 350 (Option C).