word problem: quadratic inequality?

Question

the problems are word problems, and if you have trouble with word problems, you will know my delema, when it said that they had to be converted into Quadratic inequality, and solved... i knew what both of these where, and i was just like "............what??? you want me to do what?????"
so in hopes of one of you knowing how to do this, or knowing someone that does, i am sending along the example questions....

1) if 15 persons sign up for a boat trip, the price per person will be $50. The ticket price is reduced by $2 for each additional passanger beyond 15. How many passengers will produce the maximum income, and what is the maximum income??


2) 400 people will attend a concert if tickets cost $10 each. Attendance will decreace by 20 people for each $1 increased in the price. What ticket price will yeild the maximum income, and what is the maximum income from ticket sales?


3) and apple orchard has 20 trees per acre and each tree produces an average of 200 apples. For each additional tree planted per acre, the average yeil will be reduced by 5 apples per tree. how many trees per acre will produce the maximum number of apples, and whtat is the maximum number of apples per acre?

Answer 1

1.
Let x be the number of people signed up.
Let y be the income.

income = (ticket price) * (signups)
y = (50-2(x-15))*x
y = (80-2x)*x
Obviously, this equation has roots (i.e. y=0) when x=40 or x=0, so by symmetry, the maximum is at x=20.

Maximum income is $800, when the boat has 20 passengers.


2.
Let x be the ticket price.
Let y be the income.

income = (tickets sold)*(ticket price)
y = (400-20*(x-10))*x
y = (-20x+600)*x
As above, the roots are where x=30 or x=0, so by symmetry, the maximum is at x=15.

Maximum income is $4500, when the ticket price is $15.


3.
Let x be the number of apple trees.
Let y be the total number of apples.

total apples = (apples per tree)*(number of trees)
y = (200-5(x-20)*x
y = (-5x +300)*x

As above, roots are where x=60 or x=0, so by symmetry, the maximum is at x=30.

Maximum apples is 4500 per acre, when there are 30 trees per acre.

Answer 2

ok i believe this should be the right formula for number one, but you will have to find out the answer. p=15 people, x=number of extra people.

p+x=50-2x

so 15 people plus how ever many more is equal to $50 minus $2 times the amount of how many extra people.