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≥1,700; at least 30 hours
950+25x≤1,700; at most 30 hours
950+25x≥1,300; at least 14 hours
950+25x≤1,300; at most 14 hours
950+25x≥1,700; at least 30 hours
Mary Ann solves the inequality −3x≥12
. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
Mary Ann adds −3 to both sides of the inequality to get x≥9
.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤
to get x≤−4
.
Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to negative 4 .
Mary Ann adds −3
to both sides of the inequality and changes the inequality symbol to ≤
to get x≤9
.
Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3
to get x≥−4
.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9.
Which of the following shows how to solve the linear inequality with a letter coefficient Hy<7
, where H
is a number greater than 0?(1 point)
Responses
y<7
y less than 7
y<7H
y less than Start Fraction 7 over upper H End Fraction
Hy<7
y<7
The correct linear inequality that would best translate the problem is:
950 + 25x ≥ 1,300; at least 14 hours
This inequality is obtained by adding the cost of the trip to Jorelle's savings and the earnings from tutoring, and then setting it greater than or equal to the total cost of the trip. Thus, solving this inequality will determine the minimum number of hours Jorelle must tutor.
To determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip, we need to calculate the total cost of the trip first.
The cost of the trip includes airfare, food, itineraries, and hotel expenses. We are given that the trip will cost $1,300.00. The cost of the hotel is $80.00 per night for 5 nights, which adds up to $400.00. Hence, the remaining expenses related to airfare, food, and itineraries sum up to $1,300.00 - $400.00 = $900.00.
Now let's consider Jorelle's savings and earnings. He has $950.00 in savings and he earns $25.00 per hour from his online tutoring services. Let's assume he tutors for x hours.
The total amount of money Jorelle will have for the trip is his savings plus his earnings from tutoring, which can be represented as $950.00 + $25.00x.
To have enough money for the trip, this amount must be greater than or equal to the total cost of the trip. Therefore, the linear inequality is:
950 + 25x ≥ 900.
Simplifying the inequality, we have:
25x ≥ 400.
Dividing both sides of the inequality by 25, we get:
x ≥ 16.
So, Jorelle must tutor for at least 16 hours to have enough money for the trip.
Therefore, the correct answer is:
950 + 25x ≥ 1,300; at least 16 hours.