To determine how many hours Jackson must work this week in order to have at least an extra $50 to put in his savings account after covering his spending budget, we can set up the problem as follows:
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Define Variables: Let \( h \) be the number of hours Jackson works.
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Determine Earnings: Jackson earns $25 per hour as a tutor. Therefore, his total earnings for \( h \) hours will be: \[ \text{Earnings} = 25h \]
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Set Up the Budget: Jackson has a weekly spending budget of $130. We need to determine how much he can save after covering this budget: \[ \text{Money left after spending} = \text{Earnings} - \text{Budget} = 25h - 130 \]
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Establish Savings Goal: Jackson wants to have at least an extra $50 for savings. Therefore, we can set up the inequality: \[ 25h - 130 \geq 50 \]
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Solve the Inequality: Now we will solve the inequality step-by-step. \[ 25h - 130 \geq 50 \] First, add 130 to both sides: \[ 25h \geq 50 + 130 \] \[ 25h \geq 180 \] Next, divide both sides by 25: \[ h \geq \frac{180}{25} \] Simplifying the fraction: \[ h \geq 7.2 \]
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Interpret the Result: Since Jackson cannot work a fraction of an hour, he must round up to the nearest whole number. Therefore, he must work at least: \[ h = 8 \text{ hours} \]
Conclusion: Jackson must work at least 8 hours this week in order to have at least an extra $50 to put in his savings account.
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