Frank is looking for the best deal on a television that has a wholesale price of $\$ 579$. Help him compare the price of the television at two different stores by completing the following. (a) Frank goes to a superstore that marks up the television's wholesale price $60 \%$. Ignoring tax, how much would he pay for the television at this store? (b) Frank then looks at the television in a department store that marks up the television's wholesale price $70 \%$. But because of a customer loyalty program, he would receive a $10 \%$ discount off the in-store price. Ignoring tax, how much would he pay for the television at this store? (c) Select the true statement. Frank would pay less for the television at the superstore. Frank would pay less for the television at the department store. Frank would pay the same amount for the television at the department store and at the superstore. Check Save I
Solution
Step 1 ：First, we need to calculate the price of the television at the superstore. The superstore marks up the television's wholesale price by 60%, so we need to add 60% of the wholesale price to the wholesale price itself. The calculation is as follows: \(579 + 0.6 \times 579 = 926.4\).
Step 2 ：Then, we need to calculate the price of the television at the department store. The department store marks up the television's wholesale price by 70%, and then gives a 10% discount off the in-store price. So we need to add 70% of the wholesale price to the wholesale price itself, and then subtract 10% of the result. The calculation is as follows: \((579 + 0.7 \times 579) \times (1 - 0.1) = 885.87\).
Step 3 ：Finally, we need to compare the two prices to determine where Frank would pay less for the television. The price at the superstore is \(926.4\) and the price at the department store is \(885.87\). Therefore, the statement 'Frank would pay less for the television at the department store' is true.
Step 4 ：\(\boxed{\text{Final Answer: Frank would pay less for the television at the department store.}}\)
