Tim works part-time at a retail store. His salary varies directly by the number of hours worked. Last week he earned $99.45 for 13 hours of work. This week he earned $160.65.

a. Write and solve an equation that represents this scenario.
b. How many hours did he work?

160.65 / (99.45/13) = x

1.6 a. To write the equation, let's assume that his salary varies directly with the number of hours worked. We can use the equation form: Salary = k * Hours, where k is a constant of variation.

Using the information provided, we have:
Last week: Salary = $99.45, Hours = 13
This week: Salary = $160.65, Hours = x (unknown)

The equation becomes:
99.45 = k * 13

To solve for k, divide both sides of the equation by 13:
99.45 / 13 = k
k ≈ 7.65

Now that we know k, we can use it to find the number of hours worked this week:
160.65 = 7.65 * x

b. To find the number of hours, we can rearrange the equation:
x = 160.65 / 7.65

Using a calculator, we find:
x ≈ 20.96

So, Tim worked approximately 20.96 hours this week.