Kristof is writing a book and tracks the number of hours he spends writing. He writes for 1.25 hours before breakfast each day, and has a set amount of time each afternoon to write. Kristof wants to determine how many hours he should spend writing each afternoon to meet his goal of writing for at least 35 hours this week.

Question

Create an inequality to model this situation and solve. Then, graph the solution on the number line.

Answer 1

Let x be the number of hours Kristof should spend writing each afternoon to meet his goal.

Kristof writes for 1.25 hours before breakfast each day, so the total number of hours he writes per day is 1.25 + x.

He wants to write for at least 35 hours in a week, which is 7 days.

Therefore, the total number of hours he writes in a week should be at least 35:

7(1.25 + x) ≥ 35
8.75 + 7x ≥ 35
7x ≥ 26.25
x ≥ 3.75

So, Kristof should write for at least 3.75 hours each afternoon to meet his goal of writing for at least 35 hours this week.

Graphing this solution on the number line includes all values greater than or equal to 3.75:

[3.75, ∞)