An online music club has a one-time registration fee of $20 and charges $0.50 for each song download. If Ella has $50.00 to join the club and buy songs, which inequality gives the maximum number of songs, s, she can buy?
s greater than or equal to 30
s less than or equal to 30
s greater than or equal to 60
s less than or equal to 60
Let x be the number of songs Ella can buy.
She spent 0.50x on songs.
So, her remaining money is 50 - 0.50x.
Since she also needs to pay $20 for registration, her remaining money should be greater than or equal to 20.
Thus, we have the inequality: 50 - 0.50x ≥ 20.
Simplifying this inequality, we get: 30 ≥ 0.50x.
Dividing both sides of the inequality by 0.50, we have: 60 ≥ x.
Therefore, the maximum number of songs Ella can buy is x ≤ 60.
Thus, the correct inequality is s less than or equal to 60.
can you explain the process of waht you did
Sure! Let me break down the process step by step:
1. We start by defining the variable: Let x be the number of songs Ella can buy.
2. We determine the cost of the songs: Each song costs $0.50, so the amount Ella spends on songs is 0.50x.
3. We calculate Ella's remaining money: Ella starts with $50, and we subtract the amount she spent on songs (0.50x) to find her remaining money: 50 - 0.50x.
4. We consider the registration fee: Ella also needs to pay a one-time registration fee of $20. This means her remaining money (50 - 0.50x) should be greater than or equal to $20.
5. We write the inequality: Combining the information from steps 3 and 4, the inequality is written as 50 - 0.50x ≥ 20.
6. We simplify the inequality: By subtracting 50 from both sides of the inequality, we get -0.50x ≥ -30. Then, by dividing both sides of the inequality by -0.50 (which is the same as multiplying both sides by -2 to make the coefficient of x positive), we flip the inequality sign and get 0.50x ≤ 60.
7. We express the maximum number of songs Ella can buy: The inequality 0.50x ≤ 60 implies x ≤ 60. Therefore, the maximum number of songs Ella can buy is x ≤ 60.
In conclusion, the correct inequality is s less than or equal to 60.