Answer: Hi, if the question is "how many hours she needs to work this week in order to win at least $690"
then, per week Lia wins:
$150 + $45*x,
where x is the amount of hours that she worked in the week.
then the equation we need to solve is:
$150 + $45*x = $690
$45*x = $690 - $150 = $540
x = 540/45 = 12
then she needs to work at least 12 hours this week in order to win at least $690.