I think your problem statement is a little vague. "Let x be the number of gaming systems that will be made in plant 1"-- in what time period? A day? A week? A year? Based on other information, I think we are supposed to assume the time period is a week. Then the parts of the problem begin to fit together. With this assumption, the number of hours for motherboard production per week is
so we must have
The other constraints are similar.