Over the past two weeks, Jane earned $292 and $193 respectively, at her part time job. What must she earn in the third week to bring her three-week average earnings to $200 per week?

292 + 193 = 485

Since she must earn $600 for three weeks --

600 - 485 = _____ for the third week

To find out how much Jane must earn in the third week to bring her three-week average earnings to $200 per week, we need to calculate the total earnings for the first two weeks.

First, let's add up the earnings for the first two weeks:
$292 + $193 = $485

Now, we need to determine how much Jane needs to earn in the third week to average $200 per week over the three weeks. Let's denote the third week's earnings as "x".

To find the average, we'll sum up the earnings for the three weeks and divide it by the number of weeks, which is 3 in this case.

($485 + x) / 3 = $200

To solve for "x", we can multiply both sides of the equation by 3, which will eliminate the division:

$485 + x = 3 * $200

Simplifying the right side:
$485 + x = $600

Now, we can isolate "x" by subtracting $485 from both sides of the equation:

x = $600 - $485

Finally, let's calculate the value of "x":

x = $115

Jane must earn $115 in the third week to bring her three-week average earnings to $200 per week.