Asummer 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

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200