On a quiz show you've made it to the final round. the host explains to you that you can choose from 2 prize plans. in plan a, you'll win $1,280 guaranteed, plus $40 more for each final round question you answer correctly. under plan b, you'll win only $800 guaranteed, but $100 for each question. complete the following statements (use proper number formatting, such as commas):
the plans will pay the same at
correct questions.
the amount they'll pay at that number of questions is $
.
you think you can answer 9 questions correctly. which plan should you choose?

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 be the number of questions a player gets right and let be the total money earned through the final round.

Plan A:

Plan B:

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.

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.

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"

m∠a is 90°

m∠b is 40°