Question

Derrick received a total of 21 gift cards for graduation. He received gift cards in each of four denominations (sizes), $25, $50, $75, and $100. The number of $100 gift cards Derrick got was twice the number of $75 gift cards he received. The total value of the $50 gift cards he got exceeded the total combined value of $25, $75, and $100 gift cards by $100. How many $25 gift cards did Derrick get for graduation?

A. 1
B. 2
C. 3
D. 4

Answer 1

To find the number of $25 gift cards Derrick received for graduation, we can set up and solve a system of equations. The answer is 3.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the unknown quantities. Let the number of $25 gift cards be x, the number of $50 gift cards be y, the number of $75 gift cards be z, and the number of $100 gift cards be w.

From the information given, we can create the following equations:

1. w = 2z
2. 50y = 25x + 75z + 100w + 100
3. x + y + z + w = 21

Using these equations, we can solve for the value of x, which represents the number of $25 gift cards Derrick received.

After solving the equations, we find that x = 3.