Question

Question #70266

Answer 1

Representing Ben's score on the x axis and Jim's score on the y axis, the set of all possible scores for Ben and Jim is:

Explanation:

Let's call Ben's score `b` and Jim's score `j`. We know 3 things:

`b ge 78`
`g ge 78`
`b + g le 168`

This gives us a system of inequalities with two variables. This means that the best way to represent our solution set is on a coordinate plane.

Let's put Ben's score on the x-axis. We know his score must not be less than 78, so that gives us this inequality:

Let's also put Jim's score on the y-axis. We know his score must also not be less than 78, so that gives us this inequality;

Finally, we know that their combined score cannot be greater than 168, which we can represent on this graph by the inequality `x + y le 168`

If we put all three of these inequalities on the graph at the same time, we see that there is a small area of overlap between them.

This area of overlap is our solution set. Representing Ben's score with `x` and Jim's with `y`, this area gives all possible pairs of scores for Ben and Jim.

Final Answer