Final answer:
The student's question involves translating a verbal statement into a mathematical inequality and solving for the variable. The statement 'Seven more than the quotient of a number b and 45 is greater than 5' can be expressed as the inequality (b/45) + 7 > 5, which simplifies to b > -90 when solved.
Step-by-step explanation:
The question posed by the student is a mathematical inequality problem. It asks to express the statement "Seven more than the quotient of a number b and 45 is greater than 5" as an algebraic inequality.
To translate this into an inequality we start with the quotient of b and 45, which is b/45. Next, we add 7 to this quotient, resulting in (b/45) + 7. Finally, we state that this expression is greater than 5, leading to the inequality (b/45) + 7 > 5.
To solve the inequality, we can subtract 7 from both sides, which gives us b/45 > -2. Multiplying both sides by 45 to isolate b gives us b > -90.
This establishes the solution to the student's question by providing a clear translation of the verbal statement into an inequality, and then solving the inequality for b.