Linear Inequalities Quick Check

Question

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Question
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.(1 point)
Responses

950+25x≥1,300
; at least 14 hours
950 plus 25 x greater-than-or-equal-to 1,300 ; at least 14 hours

950+25x≤1,700
; at most 30 hours
950 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours

950+25x≥1,700
; at least 30 hours
950 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 hours

950+25x≤1,300
; at most 14 hours

Answer 1

To determine the correct linear inequality and the minimum number of hours Jorelle must tutor, let's break down the problem.

Jorelle has $950 in savings and he needs a total of $1,300 for the trip. The difference he needs to cover with his tutoring income is:

\[ 1,300 - 950 = 350 \]

Now, Jorelle earns $25 per hour from tutoring. We can let \(x\) be the number of hours he tutors. His total earnings from tutoring would be \(25x\).

To have enough money for the trip, the amount he earns from tutoring plus his savings needs to be at least $1,300. Therefore, we can write the inequality as:

\[ 950 + 25x \geq 1,300 \]

Now, we need to solve for \(x\):

1. Subtract 950 from both sides: \[ 25x \geq 1,300 - 950 \] \[ 25x \geq 350 \]

2. Divide both sides by 25: \[ x \geq \frac{350}{25} \] \[ x \geq 14 \]

So, the correct linear inequality is:

\[ 950 + 25x \geq 1,300 \]

And Jorelle must tutor at least 14 hours.

Thus, the correct response is:

950 + 25x ≥ 1,300; at least 14 hours.