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.
160.65 /x = 99.45/13
x = 13 * 160.65/99.45
= 21 hours worked if constant pay per hour
To determine Tim's salary per hour, we need to use the concept of direct variation. Direct variation means that two variables are related by a constant ratio.
Let's set up the equation using the given information:
Salary = Constant * Hours
From the given information, we know that Tim earned $99.45 for 13 hours of work, so we can set up the first equation:
$99.45 = Constant * 13
To solve for the constant, we divide both sides of the equation by 13:
$99.45 / 13 = Constant
Simplifying the equation, we get:
Constant ≈ $7.65
Now, we can find Tim's salary for this week. We know that he earned $160.65, so we substitute the constant value into the equation:
$160.65 = $7.65 * Hours
To find the number of hours worked this week, we divide both sides of the equation by $7.65:
$160.65 / $7.65 = Hours
Simplifying, we get:
Hours ≈ 21
Therefore, Tim worked approximately 21 hours this week.