Applications of Inequalities Quick Check
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Question
The sum of 4.5 and one-third a number is equal to at most 38.9. What are all the possible values of the number? How would you write an inequality that could be used to solve this problem?(1 point)
Responses
4.5+13+n≤38.9, where n is equal to the number.
4.5 plus Start Fraction 1 over 3 end fraction plus n less than or equal to 38.9 , where n is equal to the number.
13n+4.5≤38.9, where n is equal to the number.
Start Fraction 1 over 3 end fraction n plus 4.5 less than or equal to 38.9 , where n is equal to the number.
13n+4.5≥38.9, where n is equal to the number.
Start Fraction 1 over 3 end fraction n plus 4.5 greater than or equal to 38.9 , where n is equal to the number.
13n+4.5=38.9, where n is equal to the number.
The correct inequality that could be used to solve this problem is: "Start Fraction 1 over 3 end fraction n plus 4.5 less than or equal to 38.9 , where n is equal to the number."
Question
The library needs at least 15 people to sign up for an event in order to run it. Currently, 3 people have signed up, and the library expects 2 more people to sign up each day. After how many days will the library be sure it can run the event? Write an inequality that could be used to solve this problem.(1 point)
Responses
2d+3≤15, where d is the number of days.
2 d plus 3 less than or equal to 15 , where d is the number of days.
3d+2≤15, where d is the number of days.
3 d plus 2 less than or equal to 15 , where d is the number of days.
3d+2≥15, where d is the number of days.
3 d plus 2 greater than or equal to 15 , where d is the number of days.
2d+3≥15, where d is the number of days.
2 d plus 3 greater than or equal to 15 , where d is the number of days.
The correct inequality that could be used to solve this problem is: "2d+3≥15, where d is the number of days."
The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 13n+4.6≤39.1 , where n equals the number, to help solve this problem. Solve his inequality.(1 point)
Responses
n≤103.5
n less than or equal to 103.5
n≤131.1
n less than or equal to 131.1
n≤112.7
n less than or equal to 112.7
n≤11.5
To solve the inequality 13n + 4.6 ≤ 39.1, we can start by subtracting 4.6 from both sides:
13n ≤ 39.1 - 4.6
Simplifying further:
13n ≤ 34.5
Finally, divide both sides by 13 to isolate n:
n ≤ 34.5/13
Therefore, the correct solution to the inequality is: n ≤ 2.65
However, since we are dealing with whole numbers, we can conclude that the possible values of the number are all whole numbers less than or equal to 2. Thus, the correct response is: n ≤ 2
The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 1/3n+4.6≤39.1 , where n equals the number, to help solve this problem. Solve his inequality.(1 point)
Responses
n≤103.5
n less than or equal to 103.5
n≤131.1
n less than or equal to 131.1
n≤112.7
n less than or equal to 112.7
n≤11.5
To solve the inequality (1/3)n + 4.6 ≤ 39.1, we can start by subtracting 4.6 from both sides:
(1/3)n ≤ 39.1 - 4.6
Simplifying further:
(1/3)n ≤ 34.5
Next, we can multiply both sides by 3 to clear the fraction:
3 * (1/3)n ≤ 3 * 34.5
Simplifying further:
n ≤ 103.5
Therefore, the correct solution to the inequality is: n ≤ 103.5