Ethan is shopping on the Internet. He is going to buy 10 songs for his brother as a gift, and some additional songs for himself. Each song costs $1.09, and Ethan can spend up to $20 in all. Which inequality can be solved for n, the number of additional songs Ethan can buy for himself? a. 1.09n-10≤20 b. 1.09n+10≤20 c. 1.09(n+10)≤20 d. 1.09(n-10)≤20

Question

Ethan is shopping on the Internet. He is going to buy 10 songs for his brother as a gift, and some additional songs for himself. Each song costs $1.09, and Ethan can spend up to $20 in all. Which inequality can be solved for n, the number of additional songs Ethan can buy for himself?                                     a. 1.09n-10≤20                                                                                                                                                                                                          b. 1.09n+10≤20                                                                                                                                                                                                        c. 1.09(n+10)≤20                                                                                                                                                                                                     d. 1.09(n-10)≤20

GPT 3.5 · Answer

a. 1.09n-10≤20

Explanation: The cost of the 10 songs for his brother is 10 x $1.09 = $10.90. To find the maximum amount Ethan can spend on additional songs for himself, we deduct $10.90 from the total amount of $20 he can spend. This gives us the inequality: 1.09n ≤ $20 - $10.90. Simplifying further, we get: 1.09n ≤ $9.10. Dividing by 1.09 on both sides, we get n ≤ 8.35. Therefore, the correct inequality is 1.09n-10≤20.