Question

Sarah has a $50 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card still have a balance of more than $30. Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.

Answer 1

Inequality: 50-1.99x=30

She has 10 days.

Explanation:

So, she starts off with with $50. From there, she is buying songs that are $1.99 (everyday). You could do this multiple ways:

Guess and Check, or use Algebra.

But for Algebra:

If we graph this out, the y intercept would be (0, 50), because she is starting out with $50. From there, she is spending 1.99 each day, so the slope would be 1.99/1. So basically, we would write this as 50-1.99x (that is the expression).

We would also set this equal to 30, because we are trying to see how many days it would take to still keep her balance above $30, but make it as close to 30 as possible. (x represents the # of days.

So the inequality would be 50-1.99x=30

And, when we isolate the variable and solve, we would see that she can buy a total of 10 songs over 10 days. (So basically, she has 10 days to stay over $30).