Find max value of (80-2x)(50-2x)x using cauchy's inequality

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be bale to prepare using the sauce?

I'm at a bookstore with $\$35$ in my pocket and a $20\%$-off coupon. what is the cost of the most expensive book i can buy with my money and the coupon? (assume that there are books of every possible price in the bookstore. it's a large bookstore! )

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?