To calculate Arin's next paycheck after receiving a dollar raise, we first need to determine his total earnings before the raise and then include the raise.
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Calculate the hours worked in a week: \[ 3 \frac{1}{2} \text{ hours} = 3.5 \text{ hours} \]
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Calculate the weekly pay before the raise: \[ \text{Weekly pay} = \text{hours worked} \times \text{hourly rate} \] \[ \text{Weekly pay} = 3.5 \text{ hours} \times 7.25 \text{ dollars/hour} = 25.375 \text{ dollars} \]
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Calculate the total pay for four weeks: \[ \text{Total pay for 4 weeks} = \text{Weekly pay} \times 4 \] \[ \text{Total pay for 4 weeks} = 25.375 \text{ dollars} \times 4 = 101.50 \text{ dollars} \]
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Calculate the new hourly rate after the raise: \[ \text{New hourly rate} = 7.25 \text{ dollars} + 1.00 \text{ dollar} = 8.25 \text{ dollars} \]
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Calculate the new weekly pay with the raise: \[ \text{New weekly pay} = 3.5 \text{ hours} \times 8.25 \text{ dollars/hour} = 28.6875 \text{ dollars} \]
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Calculate the total pay for four weeks after the raise: \[ \text{Total pay for 4 weeks after raise} = 28.6875 \text{ dollars} \times 4 = 114.75 \text{ dollars} \]
So, after receiving a dollar raise in his hourly wage, Arin will be paid $114.75 in his next paycheck.