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Have you ever seen the popular TV game show The Price Is Right? The idea is to guess the price of an item. You win the item by coming closest to guessing the correct price of the item without going over. If your opponent goes first, a good strategy is to overbid her regularly by a small amount, say \(\$ 20 .\) Then your opponent can win only if the price falls in that \(\$ 20\) region between her bid and yours. a. Write a verbal rule to determine your bid if your opponent bids first. b. Which bid is the input variable and which is the output variable in the verbal rule? Choose letters to represent your bid and your opponent's bid. c. Translate your verbal rule into an equation, using the letters you chose in part b to represent the input and output variables. d. Use your equation to determine your bid if your opponent bid \(\$ 575\) on an item. e. If you bid \(\$ 995\) on a laptop computer, use your equation to determine your opponent's bid if he went first.

Step by step solution

01

a. Writing the verbal rule

You should take your opponent's bid and add $20 to it as your bid. In this way, you can choose a value slightly higher than the opponent's bid, without going over the price, according to the given strategy.

02

b. Understanding input and output variables in the verbal rule

Here, the opponent's bid is the input variable, and your bid will be the output variable. Let us use the letters O for the opponent's bid and Y for your bid.

03

c. Translating the verbal rule into an equation

The equation representing the verbal rule is : Y = O + 20

04

d. Using the equation to find your bid when the opponent bids $575

If the opponent bids $575, we plug the value into our equation: Y = 575 + 20 Y = 595 So, in this specific case, you should bid $595.

05

e. Using the equation to find the opponent's bid when you bid $995

If your bid is $995, we have to rearrange our equation to solve for the opponent's bid: Y = O + 20, so O = Y - 20 Now, we plug your bid value into the equation: O = 995 - 20 O = 975 In this case, your opponent's bid was $975 if he went first.

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