Question

Max pays 50 per lesson plus 15 for sheet music. Maya pays a lower membership price because she’s had a music membership for 8 years. She pays a higher price for sheet music because she purchased the advanced package. Maya pays 35 per lesson plus 45 for sheet music.Create and solve an equation that can be used to determine the number of lessons Max and Maya need to receive in order for them to pay the same amount.

Answer 1

Max and Maya will pay the same amount after receiving 2 lessons each, as determined by solving the equation 50x + 15 = 35x + 45, which represents their respective costs per lesson and sheet music.

Step-by-step explanation:

To determine the number of lessons Max and Maya need to receive in order for them to pay the same amount, we need to set up an equation based on the cost structure provided for each student. Max pays $50 per lesson plus $15 for sheet music, while Maya pays $35 per lesson plus $45 for sheet music. Let's denote the number of lessons both students take with the variable x.

The total amount Max pays can be written as the equation Max's Total Cost = $50x + $15. Similarly, the total amount Maya pays can be written as the equation Maya's Total Cost = $35x + $45. We are looking for the point where these two costs are equal.

Now, we can set up the equation to find x:

50x + 15 = 35x + 45,

Solving for x gives us the following steps:

1. Subtract 35x from both sides: 50x - 35x + 15 = 45,
2. Combine like terms: 15x + 15 = 45,
3. Subtract 15 from both sides: 15x = 30,
4. Divide both sides by 15: x = 30/15,
5. Simplify: x = 2.

Therefore, after 2 lessons, both Max and Maya will have paid the same amount for their music lessons and sheet music.