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?
A4.5+1/3+n≤38.9, where n is equal to the number.
B1/3n+4.5≥38.9, where n is equal to the number.
C1/3n+4.5≤38.9, where n is equal to the number.
D1/3n+4.5=38.9, where n is equal to the number.
To express the given situation as an inequality, you want to capture the statement, "The sum of 4.5 and one-third of a number is equal to at most 38.9."
Option C is the correct way to write this inequality:
1/3n + 4.5 ≤ 38.9, where n is equal to the number.
This inequality states that one-third of the number, n, when added to 4.5, is less than or equal to 38.9.
To solve for n:
1/3n ≤ 38.9 - 4.5
1/3n ≤ 34.4
Now, multiply both sides by 3 to solve for n:
n ≤ 3 * 34.4
n ≤ 103.2
So, the possible values of n are all real numbers less than or equal to 103.2.
A4.5+1/3+n≤38.9, where n is equal to the number.
B1/3n+4.5≥38.9, where n is equal to the number.
C1/3n+4.5≤38.9, where n is equal to the number.
D1/3n+4.5=38.9, where n is equal to the number.
Apologies for any confusion previously. From the options provided:
Option C correctly represents the given statement as an inequality:
C) 1/3n + 4.5 ≤ 38.9, where n is the number.
This is the correct choice because it adheres to the conditions provided, which state that the sum of 4.5 and one-third of a number should be no more than 38.9. The inequality reflects that "at most" implies less than or equal to (≤).
Options A, B, and D do not correctly represent the given statement:
A) The presence of "+n" in the inequality is incorrect and doesn't match the given statement.
B) This inequality suggests the sum must be greater than or equal to 38.9, which is the opposite of what the statement requires.
D) This equation suggests the sum must be exactly 38.9, which does not allow for it to be less than 38.9 as the statement allows.
So, the correct choice and the most appropriate inequality to use for this problem is:
C) 1/3n + 4.5 ≤ 38.9
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.
A 2d+3≤15, where d is the number of days.
B 3d+2≥15, where d is the number of days.
C 3d+2≤15, where d is the number of days.
D 2d+3≥15, where d is the number of days.
To set up the inequality, you need to determine the number of people who will have signed up after a certain number of days, knowing that 3 people have already signed up and that 2 more people are expected to sign up each day.
Let d represent the number of days that pass.
Since 2 people sign up each day, the total number of people that have signed up after d days is the current number of people (3) plus twice the number of days (2d). The event requires at least 15 people, so the library needs the total number of sign-ups to be greater than or equal to 15 to be sure it can run the event.
This gives us the inequality:
2d + 3 ≥ 15, where d is the number of days.
So, the correct answer is:
D) 2d + 3 ≥ 15, where d is the number of days.
To find out after how many days the library will be sure it can run the event, you would solve the inequality:
2d + 3 ≥ 15
2d ≥ 12
d ≥ 6
So, after 6 days, the library will be sure it can run the event, as there will be at least 15 people signed up in total (3 initially plus 12 from the 6 days).
A 2d+3≤15, where d is the number of days.
B 3d+2≥15, where d is the number of days.
C 3d+2≤15, where d is the number of days.
D 2d+3≥15, where d is the number of days.
From the options you've provided, we're looking for an inequality that represents the scenario where the library needs at least 15 people to sign up for the event. Currently, 3 people are signed up, and the library expects an additional 2 people to sign up each day.
Let d represent the number of days after the current moment.
The relationship between the number of days and the total number of people signed up can be expressed as follows: the current number of people (3) plus twice the number of days times 2 people per day (2d).
The library needs at least 15 people to run the event, so the number of people after d days (3 + 2d) must be greater than or equal to 15. This is represented by the inequality:
2d + 3 ≥ 15
This inequality states that after d days, the number of participants (2d + 3) should be at least 15.
Therefore, the correct inequality you should use to represent this situation is:
D) 2d + 3 ≥ 15, where d is the number of days.
Using this inequality, you could solve for d to find out how many days it will be before the library has enough people to run the event.