Question

Michael is packing for a business trip and can fit at most 12 shirts in his suitcase. He wants to pack at least twice as many collared

shirts as T-shirts in the suitcase.
When c represents the number of collared shirts and t represents the number of T-shirts Michael packs in the suitcase, these
constraints are represented by the system of inequalities below.
c+t≤ 12
c≥ 2t
The system of inequalities that represents this situation is graphed on the coordinate plane. Which arrow points to the solution region?

Answer 1

Based on the given graph, the arrow that points to the solution region is the one in the region shaded in light blue colour. It is within the intersection of the two inequalities.

How to determine the solution region

The system of inequalities c + t ≤ 12 and c ≥ 2t represents the constraints for Michael's packing situation.

Let's analyze the inequalities:

c + t ≤ 12: This inequality limits the total number of shirts (collared shirts + T-shirts) to be at most 12. It defines the upper boundary for the solution region.

c ≥ 2t: This inequality ensures that the number of collared shirts (c) is at least twice the number of T-shirts (t) packed. It defines the lower boundary for the solution region.

The solution region will lie within the intersection of these two inequalities. It will be the shaded region where the constraints of both inequalities are simultaneously satisfied. It will be a region in the coordinate plane bounded by a line (representing c + t = 12) and another line (representing c = 2t).

To determine which arrow points to the solution region, look for the region of overlap or intersection of the shaded regions that satisfy both inequalities. The arrow pointing towards this region would indicate the solution region for Michael's packing situation.

Answer 2

Blue region

Explanation:

Given variables:

• Let c represent the number of collared shirts Michael packs in the suitcase.
• Let t represent the number of T-shirts Michael packs in the suitcase.

Given that Michael can fit at most 12 shirts in his suitcase, this can be represented by the following inequality:

`c+t\leq 12`

Rearrange the inequality to isolate c:

`c\leq -t+12`

Given that Michael wants to pack at least twice as many collared shirts as T-shirts in the suitcase, then:

`c\leq 2t`

When graphing inequalities:

• For < or > use a dashed line.
• For ≤ or ≥ use a solid line.
• For < or ≤ shade under the line.
• For > or ≥ shade above the line.

Therefore, the graph of c ≤ -t + 12 is:

• A solid line.
• A negative slope (as x increases, y decreases).
• Shading below the line.

So, this inequality is represented by the red line on the provided graph.

The graph of c ≤ 2t is:

• A solid line.
• A positive slope (as x increases, y increases).
• Shading below the line.

So, this inequality is represented by the blue line on the provided graph.

The overlapping shaded region of the two inequalities represents the solution of the system of inequalities. Therefore, the overlapping shaded region below the red and blue lines is the blue region.