Question

Sam has a collection of yellow and red cards. Yellow cards are worth 3 points and

red cards are worth 5 points. He has at most 15 cards, totaling at least 45 points.
This can be modeled by the following system.

y + r < 15
3y + 5r > 45

Graph the system. Then use the graph to determine which combination is a
solution.
1. 3 yellow and 9 red
2. 6 yellow and 4 red
3. 9 yellow and 3 red
4. 12 yellow and 8 red

Answer 1

Answer:1.

1. 3 yellow and 9 red

Explanation:

• r, the amount of red cards, is represented ox x-axis

• y, the amount of yellow cards, is represented ox y-axis

In the picture attached, the system is represented. The darker area shows all the points that are a solution to the system of inequalities.

The combinations can be rewritten as a coordinate pair, as follows:

1. 3 yellow and 9 red -> (9,3)

2. 6 yellow and 4 red -> (4,6)

3. 9 yellow and 3 red -> (3,9)

4. 12 yellow and 8 red -> (8,12)

As we can see in the picture, only the first option is a solution.