Question

Kaylee has a $20 gift card to spend at an online entertainment store. The table shows the categories of items she can buy. Kaylee wants to buy only songs and TV episodes with her card. If Kaylee buys at least 4 TV episodes, what combinations of songs and TV episodes can she afford? Use inequalities to justify your reasoning
App: $0.99
Song*: $1.29
TV episode: $2.99
Movie: 9.99
*This week's special: Buy six songs and get one free!

Answer 1

Answer:

  see the attached

Step-by-step explanation:

The total cost of Kaylee's purchases will be the sum of products of the number bought and the cost of the item bought. She wants this total to be at most $20. In math terms, where x and y represent songs and TV episodes, the inequalities describing the scenario are ...

• 1.29x +2.99y ≤ 20
• x ≥ 0
• y ≥ 4

The attached graph shows a plot of this set of inequalities with the feasible region shaded red. The combinations of songs and TV episodes Kaylee can afford are shown by the coordinates of the red dots in the feasible region.

According to the "special," if Kaylee buys 6 songs (and 4 TV episodes), she will get a 7th song free. That is, the "special" means point (6, 4) becomes (7, 4) if there is a 7th song that Kaylee wants.