To determine the minimum number of hours Jorelle must tutor to fund his vacation, we'll outline the problem step by step before finding the correct linear inequality.
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Total Cost Calculation:
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Jorelle's trip costs $1,300.
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He plans to stay in a hotel room for 5 nights at a rate of $80 per night.
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So, the total cost for the hotel will be:
\[ \text{Total hotel cost} = 80 \text{ (cost per night)} \times 5 \text{ (nights)} = 400 \]
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Combining this cost with the overall trip cost:
\[ \text{Total trip cost} = 1,300 + 400 = 1,700 \]
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Calculating shortfall:
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Jorelle has $950 in savings. To find the amount he needs to earn:
\[ \text{Amount needed} = 1,700 - 950 = 750 \]
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Earnings equation:
- Jorelle earns $25 per hour from online tutoring. Let \( x \) be the number of hours he needs to tutor.
- His earnings from tutoring can be represented as \( 25x \).
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Setting up the inequality:
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The money he has plus the money he earns from tutoring must be at least the total cost of the trip:
\[ 950 + 25x \geq 1,700 \]
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Solving for x:
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Rearranging the inequality:
\[ 25x \geq 1,700 - 950 \] \[ 25x \geq 750 \] \[ x \geq \frac{750}{25} \] \[ x \geq 30 \]
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So, Jorelle must tutor at least 30 hours.
Now, we compare this with the provided choices:
- A: \( 950 + 15x \geq 1,700; \text{ at least } 30 \text{ hours} \) - Incorrect (wrong coefficient for x)
- B: \( 950 + 25x \leq 1,700; \text{ at most } 30 \text{ hours} \) - Incorrect (inequality direction and conclusion)
- C: \( 950 + 25x \geq 1,300; \text{ at least } 14 \text{ hours} \) - Incorrect (doesn't reflect the correct total cost)
- D: \( 950 + 25x \leq 1,300; \text{ at most } 14 \text{ hours} \) - Incorrect (wrong total)
None of the options correctly reflect the situation described. The correct inequality based on our analysis is:
\[ 950 + 25x \geq 1,700 \]
The minimum number of hours Jorelle must tutor is 30.