Final answer:
The system of equations that describes the number of middle school prizes (x) and the number of high school prizes that Dre can purchase is option b: x + y ≥ 50; 2x + 3y ≤ 14.
Step-by-step explanation:
The system of equations that describes the number of middle school prizes (x) and the number of high school prizes that Dre can purchase is option b: x + y ≥ 50; 2x + 3y ≤ 14.
To understand why, let's break down the options:
- a. x + y ≤ 14 ; 3x + 2y ≥ 50: This option restricts the number of middle school prizes (x) and does not provide any restriction on the number of high school prizes (y), so it does not describe the relationship between the two.
- b. x + y ≥ 50; 2x + 3y ≤ 14: This option states that the sum of middle school prizes (x) and high school prizes (y) should be greater than or equal to 50. Additionally, it restricts the combined number of prizes (x + y) to be less than or equal to 14. Therefore, this option accurately describes the relationship between the two types of prizes.
- c. x + y ≥ 14 ; 2x + 3y ≤ 50: This option restricts the sum of middle school prizes (x) and high school prizes (y) to be greater than or equal to 14. However, it does not provide any restriction on the combined number of prizes (x + y), so it does not accurately describe the relationship between the two.
- d. x + y ≥ 50; 2y - 3x ≥ 14: This option states that the sum of middle school prizes (x) and high school prizes (y) should be greater than or equal to 50. However, it provides a different restriction on the relationship between the two types of prizes (2y - 3x ≥ 14), which does not accurately describe their relationship.