Understanding Systems of Inequalities

Luis has a $25 gift card for an online retailer selling digital music and games. Each song costs $1, and each game costs $2. He wants to buy at least 15 items. The video sets up a system of inequalities to represent this scenario and uses a graph to identify possible purchase combinations. Variables are defined, and constraints are established. The graph is analyzed to find the range of valid combinations of songs and games that Luis can purchase without exceeding the gift card limit.

What is the total value of the gift card Luis received?

• $20

• $30

• $25

• $15

Tags

CCSS.6.EE.B.7

How much does each game cost?

• $4

• $3

• $2

• $1

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CCSS.7.EE.B.4B

What is the minimum number of items Luis wants to purchase?

• 10

• 20

• 15

• 12

If 's' represents songs and 'g' represents games, which inequality represents the total number of items Luis wants to buy?

• s + g > 15

• s + g < 15

• s + g ≤ 15

• s + g ≥ 15

What is the inequality for the total cost Luis can spend?

• s + 2g ≤ 25

• s + 2g > 25

• s + 2g ≥ 25

• s + 2g < 25

Tags

CCSS.HSA.REI.D.12

In the graph, what does the line s = -g + 15 represent?

• The cost constraint

• The boundary for songs

• The item constraint

• The boundary for games

What is the s-intercept of the line s = -g + 15?

• 10

• 15

• 25

• 20

Which point would not satisfy the inequality s + g ≥ 15?

• (5, 10)

• (15, 0)

• (10, 5)

• (0, 0)

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CCSS.8.F.A.3

CCSS.8.EE.B.6

What is the g-intercept of the line s = -2g + 25?

• 20

• 12.5

• 10

• 15

Tags

CCSS.HSA.REI.D.12

Which region on the graph represents the solution to the system of inequalities?

• Above both lines

• Below both lines

• Between the lines

• Outside the lines

Tags

CCSS.HSA.REI.D.12