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Becky and Michele are both shopping for a new car at two different dealerships. Dealership A is offering $500 cashback on any purchase, while dealership B
is offering $1,000 cash back. The tax rate is 5% at dealership A but 8% at Dealership B. Becky wants to buy a car that is $15,000, and Michele is planning to buy a car that costs $20,000. Use algebraic expressions to help you answer the following question.
1. At which dealership will Becky get the better deal? how much does she save?
2. At which dealership will Michele get the better deal? how much does she save?
3. What gerneralization can you make that would help any shopper know which dealership has the better deal? At which price point would the two deals be equal.

Answer :

Becky will get the better deal at B. ($15,200 total) SHE saves $50
15,000 × .08 = 1,200
1,200 + 15,000 = 16,200
16,200 - 1000 = 15,200
While Michele will get the better at A($20,500total) SHE saves $100
20,000 × .05 = 1,000
1,000 + 20,000 = 21,000
21,000 - 500 = 20,500

3. The higher the price, go to A. the lower the price go to be. the midpoint is

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