Answer:
1) "The plans will pay the same at 8 correct questions"
2) "The amount they'll pay at that number of questions is $1600"
3) "You think you can answer 9 questions correctly. Which plan should you choose? Plan B."
Step-by-step explanation:
We can represent each of the two prize plans with a linear equation. Let [tex]q[/tex] be the number of questions a player gets right and let [tex]d[/tex] be the total money earned through the final round.
Plan A: [tex]1280 + 40q = d[/tex]
Plan B: [tex]800 + 100q = d[/tex]
1) Since these are linear equations (ie. lines), we can find the intersection in two ways.
(1) Plot a graph
(2) Set equations equal to each other.
I will show (2) but you can confirm by plotting these two lines on a graph.
[tex]1280 + 40 q = 800 + 100q\\1280 - 800 = 100q - 40 q\\480 = 60q\\q = 8[/tex]
This means that if you get 8 questions correct, both prize plans will return the same amount of money. Therefore the first question is...
"The plans will pay the same at 8 correct questions"
2) To answer the second statement we simply plug in 8 into either equation. Remember at 8 questions, both prizes give you the same amount of money, so it doesn't matter which equation we select. I will plug 8 into Plan B.
[tex]800 + 100(8) = d\\d = 1600[/tex]
So the second question's answer is...
"The amount they'll pay at that number of questions is $1600"
3) To answer the third and final question. We can simply plug in 9 into each equation and compare. However, a shortcut is to notice that Plan B will give more money for each correct answer. And since 9 questions is greater than our point of intersection 8, Plan B will result in more money.
"You think you can answer 9 questions correctly. Which plan should you choose? Plan B"
