We know that Mr. Jackson charges $75 for each car he details and $25 for each car wash. Let's write an expression for his earnings for detailing y cars and washing x cars.
75y+25xWhat combination of car washing and car detailing would earn him the most amount of money? We know that he works at most 8 hours per day. Therefore, he would definitely earn the most when working the full 8 hours. Additionally, we have been given an inequality for the time he works.
y ≤ -1/3x+8
This inequality represents the amount of car washing and detailing he can do in an 8 hour day. If he works exactly 8 hours, this inequality will become an equation. This equation represents the maximum amount of money he can earn! Let's substitute y= - 13x+8 into our expression to find the maximum amount.
