Question

an exam consists of two parts. section x and y. there can be a maximum of 90 questions. there must be at least 5 more questions in section y than in section x. write a system of inequalities to model the number of questions in each of the two sections. then solve the system by graphing

Answer 1

an exam consists of two parts. section x and y. there can be a maximum of 90 questions. there must be at least 5 more questions in section y than in section x. write a system of inequalities to model the number of questions in each of the two sections. then solve the system by graphing

Answer 2

To start, you know that x+y=90 (max of 90 questions). Then you know that since y has to have at least 5 more questions than x, \[y\ge x+5\]
Now you have two equations and two unknowns, you can solve for each. Set y=90-x (from first eqn) and put that into the 2nd eqn. Solving for x you end up with \[x \le 42.5\] And since you need to have at least one question in x, and you can't have half questions, \[1 \le x \le 42\] and \[47 \le y \le 89\]

Answer 3

so that is the answer