Mikel has a chance to win a trip on a TV game show. All he has to do is win the “Shopping Game”. In this game, Mikel is shown six grocery store items without being shown the prices. He must buy multiples of items until he has a total between $20 and $21 inclusive. If he doesn’t reach $20 with his first item, he continues buying items and adding to his total, until he either wins by getting an amount between $20 and $21, or he loses by going over $21 or by buying all items and being less than $20. First, Mikel buys six bottles of shampoo.
1. Write a compound inequality to find the range of prices for one bottle of shampoo that would make Mikel win instantly.
2. Solve the compound inequality. Round each answer to the hundredths place.
3. In your work for number 6, you should have gotten a repeating decimal. Explain how you decided to round this number up or down.