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Let's break down the problem into two parts: the amount of money Michele saves each week and the total amount of money she has saved.
Let's represent the amount of money Michele saves each week as x.
After 2 weeks, the total amount of money she has saved is 2x.
After 7 weeks, the total amount of money she has saved is 7x.
According to the problem, she has $55 after 2 weeks, so we can represent this as:
2x = 55
According to the problem, she plans to have $105 after 7 weeks, so we can represent this as:
7x = 105
So the equation for the problem is the system of equations:
2x = 55
7x = 105