Question

Drew is a counselor at a summer camp and needs to buy prizes for the competitions at the end of the week.

- There are two groups, middle school and high school, for which he needs prizes.
- He wants to buy at least 14 prizes but to spend no more than $50
- Drew finds fun middle school prizes for $2 each and high school prizes for $3 each. Which system of equations describes the number of middle school prizes (2 ) and the number of high school prizes (y) that Drew can purchase?
a. x+y≤ 14; 3x+2y≥ 50
b. x+y≥ 50; 2x+3y≤ 14
c. x+y≥ 14; 2x+3y≤ 50
d. x+y≥ 50; 2y-3x≥ 14

Answer 1

The correct system of equations for the number of middle school prizes (x) and high school prizes (y) with Drew's constraints is c. x+y≥ 14; 2x+3y≤ 50.

Step-by-step explanation:

The question asks which system of equations describes the number of middle school prizes (x) and high school prizes (y) that Drew can purchase given his constraints. Drew wants to buy at least 14 prizes but spend no more than $50, with middle school prizes costing $2 each and high school prizes costing $3 each.

The system of equations that describes the number of middle school prizes (2x) and the number of high school prizes (y) that Drew can purchase is: a. x+y≤ 14; 3x+2y≥ 50

To determine this, we need to set up inequalities based on the given information. The first inequality is x + y ≤ 14, which means the sum of the middle school prizes and high school prizes must be less than or equal to 14. The second inequality is 3x + 2y ≥ 50, which means the total cost of middle school prizes ($2 each) and high school prizes ($3 each) must be greater than or equal to $50.

The correct system of equations is c. x+y≥ 14; 2x+3y≤ 50. This represents the situation accurately: Drew needs at least 14 prizes (x+y≥ 14), and he cannot spend more than $50 on the prizes (2x+3y≤ 50).

Therefore answer is c. x+y≥ 14; 2x+3y≤ 50.