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 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 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≥1,300; at least 14 hours
950 plus 25 x greater-than-or-equal-to 1,300 ; at least 14 hours
950+25x≤1,300; at most 14 hours
950 plus 25 x less-than-or-equal-to 1,300 ; at most 14 hours
The correct answer is:
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 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 divides both sides of the inequality by negative 3 to get x greater-than-or-equal-to negative 4 .
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 .
The correct answer is:
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 point)
Responses
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 less than y .
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y.
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1 greater than y .
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144 less than y .
Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
The correct answer is:
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y.
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<7H
y less than 7 upper H
y<7
y less than 7
Hy<7
upper H y less than 7
y<7H
The correct answer is:
y<7/H
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses
Bx
upper B x
72
72
x
x
B
The correct answer is:
Bx
To determine the minimum number of hours Jorelle must tutor to have enough money for the trip, we need to calculate the total cost of the trip and then subtract his savings.
First, let's calculate the total cost of the trip. The airfare, food, and itineraries cost $1,300.00. Additionally, Jorelle plans to stay in a hotel room for 5 nights at a cost of $80.00 per night. So, the cost of the hotel room would be 5 * $80.00 = $400.00.
Therefore, the total cost of the trip is $1,300.00 + $400.00 = $1,700.00.
Now, we can set up a linear inequality in one variable to represent the situation. Let's use the variable x to represent the number of hours Jorelle must tutor. Since he earns $25.00 per hour, the amount of money he earns from tutoring would be 25x.
To have enough money for the trip, he must earn at least $1,700.00. So, the linear inequality would be:
950 + 25x ≥ 1,700
This inequality represents that Jorelle's savings of $950 plus the money he earns from tutoring (25x) should be greater than or equal to the total cost of the trip ($1,700.00).
To determine the minimum number of hours Jorelle must tutor, we can solve this inequality.
Thus, the correct answer is:
950+25x≥1,700; at least 30 hours