Question

Staci has $20 Apps Cash card and wants to buy some games and songs. Each game costs $2 and each song costs $1. Staci wants to buy at least 12 items. Solve the system of inequalities by graphing to determine the possible numbers of games and songs that Staci can buy

Answer 1

• 8 or fewer games
• 4 or more songs
• the solution space is the doubly-shaded area of the graph

Explanation:

You want the graphical solution to the set of inequalities that describes the numbers of games (x) and songs (y) that Staci can buy with $20, if a game costs $2 and a song costs $1, and Staci wants to buy at least 12 items.

Inequalities

The inequalities that describe the numbers are ...

2x +y ≤ 20 . . . . . Staci has at most $20 to spend

x + y ≥ 12 . . . . . . Staci wants to buy at least 12 items

Graph

Each of these inequalities has a solid boundary line on its solution space graph. The shading is below the line for the first inequality, and above the line for the second one. The vertices of the triangular solution space are ...

(0, 12), (0, 20), (8, 4)

Possible numbers are the coordinates of any grid point within the triangle or on its boundaries.