Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Question 8 options:
Let x be the number of days Sarah uses the gift card to buy song downloads.
The amount of money Sarah spends on song downloads per day can be represented by the expression 1.99x.
The amount of money remaining on the gift card after x days can be represented by the expression 30 - 1.99x.
According to the prompt, the gift card should still have a balance of more than $18. This can be represented by the inequality 30 - 1.99x > 18.
Now we can solve the inequality:
30 - 1.99x > 18
-1.99x > 18 - 30
-1.99x > -12
x < -12 / -1.99
x < 6.03
Since the number of days (x) must be a whole number, Sarah can have a balance of more than $18 on her gift card for a maximum of 6 days.
The solution to the inequality means that if Sarah uses the gift card to buy song downloads for more than 6 days, the remaining balance will be less than $18. Conversely, if Sarah uses the gift card for 6 days or less, the gift card will have a balance of more than $18.