Question

You have $30 to spend on downloading songs for your iPod. Company A charges $0.79 per song and Company B charges $0.99 per song. Write an equation that models this situation

Answer 1

To model the song downloading situation with a budget of $30, we use the equations 0.79x <= 30 for Company A and 0.99x <= 30 for Company B, where x is the number of songs.

Step-by-step explanation:

To model the situation where a student has $30 to spend on downloading songs, we can write two separate linear equations, one for each company. For Company A, which charges $0.79 per song, the equation will be:

0.79x ≤ 30

Where x represents the number of songs the student can download from Company A. For Company B, which charges $0.99 per song, the equation will be:

0.99x ≤ 30

Again, x represents the number of songs the student can download from Company B, but the cost per song is different, hence a different equation.

These equations are used to determine the maximum number of songs the student can download from each company without exceeding the $30 budget.

Answer 2

Let x = the number of songs you can buy.

If you use company A at 0.79 dollars per song, your variable is 0.79x. If you use company B at 0.99 dollars per song, your variable is 0.99x. You are going to set both equal to 30.

Company A: 0.79x = 30

Company B: 0.99x = 30

When solving (though I know you didn't ask), do note that you cannot buy part of a song so you would need to round down to the nearest whole number.

So if you use company A, you divide both sides by 0.79 to isolate the variable x and satisfy the division principle of equality:

x = 30/0.79.

Simplify and your answer is 37.97, round down to 37 songs; you'd have 37 songs with company A and 77 cents left over in your account just sitting there because what really can you do with 77 cents on the App Store?