To determine how much money Michael will have 10 weeks after opening his bank account, we first need to figure out the rate at which his account balance is increasing.
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Initial balance: $100
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Balance after 5 weeks: $250
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Increase in balance over 5 weeks:
\[ 250 - 100 = 150 \]
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Rate of increase per week:
\[ \text{Rate} = \frac{150}{5} = 30 \]
This means Michael's account is increasing by $30 each week.
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Total time after opening the account: 10 weeks.
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Total increase over 10 weeks:
\[ \text{Increase over 10 weeks} = 30 \times 10 = 300 \]
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Total balance after 10 weeks:
\[ \text{Total balance} = 100 + 300 = 400 \]
Therefore, 10 weeks after opening the account, Michael will have $400.