Question

A summer camp cookout is planned for the campers and their families. There is room for 525 people. Each adult costs $9, and each camper costs $5. There is a maximum budget of $1,200. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.

x + y ≤ 525
5x + 9y ≤ 1,200
x + y ≤ 1,200
5x + 9y ≤ 525
x + y ≤ 525
9x + 5y ≤ 1,200
x + y ≤ 1,200
9x + 5y ≤ 525

Answer 1

The system of inequalities to represent this real-world scenario is x + y ≤ 525 and 5x + 9y ≤ 1,200. The first inequality represents the maximum number of people that can attend the cookout, and the second inequality represents the budget constraint.

Step-by-step explanation:

The system of inequalities to represent this real-world scenario is:

x + y ≤ 525

5x + 9y ≤ 1,200

The first inequality represents the maximum number of people that can attend the cookout, which is 525. The second inequality represents the budget constraint, where the cost for adults (represented by x) is $9 and the cost for campers (represented by y) is $5. The maximum budget is $1,200. The system of inequalities ensures that the number of people does not exceed the maximum capacity and that the total cost does not exceed the budget.

Answer 2

Let:
x = numbers of adults
y = numbers of campers
We know that each adults (x) cost $9, so it’s 9x.
We also know that we act camper (y) cost $5, so it’s 5y.
There is a budget of $1,200, thus the cost of x and y must less than or equal to $1,200.
Therefore we have 9x + 5y ≤ $1,200

We also know that the number of people are 525, so the number of camper and adult must less than or equal to the sum of all people. Therefore, we have
x + y ≤ 525

Answer : 9x + 5y ≤ $1,200 and x + y ≤ 525