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)
O 4.5 + ‡ + n 5 38.9, where n is equal to the number.
0 =n +4.5 ≥ 38.9, where n is equal to the number.
O In +4.5 = 38.9, where n is equal to the number.
0 In + 4.5 < 38.9, where n is equal to the number.
The correct inequality that could be used to solve this problem is:
4.5 + (1/3)n ≤ 38.9
This inequality represents the sum of 4.5 and one-third of a number (n) being less than or equal to 38.9.
Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality &n - 12 > 24, where n equals the number, to help solve this problem. Solve her inequality. (1 point)
• n > 9.6
On > 45
O n > 15
O n > 28.8
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)
• 2d + 3 < 15, where d is the number of days.
• 3d + 2 < 15, where d is the number of days.
• 3d + 2 ≥ 15, where d is the number of days.
• 2d + 3 > 15, where d is the number of days.
The correct inequality that could be used to solve this problem is:
3 + 2d ≥ 15
This inequality represents the number of people signed up (3) plus 2 times the number of days (d) being greater than or equal to 15.
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 §n + 4.6 < 39.1, where n equals the number, to help solve this problem. Solve his inequality. (1 point)
On < 103.5
O n < 131.1
On < 11.5
On < 112.7
To solve the inequality &n - 12 > 24, where n is the number, we can start by adding 12 to both sides of the inequality:
n > 24 + 12
Simplifying the right side gives:
n > 36
So, the correct answer is:
n > 36
Ellie is saving to buy a phone. She wants to have at least $299 saved before buying one. She currently has $213 saved, and she receives $10 a week as an allowance from her parents. After how many weeks will Ellie have enough money saved? Ellie writes the inequality 10w + 213 > 299, where w is the number of weeks, to help figure this out. Solve her inequality.
(1 point)
O w > 51.2
О w > 8.6
O w > 860
O w > 86
To solve the inequality 10w + 213 > 299, where w is the number of weeks, we can start by subtracting 213 from both sides of the inequality:
10w > 299 - 213
10w > 86
Then, we can divide both sides of the inequality by 10 to solve for w:
w > 86/10
w > 8.6
So, Ellie will have enough money saved after at least 9 weeks.
The correct answer is: w > 8.6
To find the possible values of the number, let's break down the problem step by step:
Step 1: Define the number
Let's say the number is "n".
Step 2: Express the statement mathematically
The sum of 4.5 and one-third of a number (n) can be written as:
4.5 + (1/3)*n
Step 3: Write an inequality to represent the problem
According to the problem, the sum described above is equal to AT MOST 38.9. The phrase "at most" indicates a less than or equal to comparison. Therefore, the inequality that represents this problem is:
4.5 + (1/3)*n ≤ 38.9
This inequality states that the sum of 4.5 and one-third of the number (n) is less than or equal to 38.9.
Now, let's review the answer choices:
O 4.5 + ‡ + n 5 38.9, where n is equal to the number.
Incorrect. This equation is not correct as it does not reflect the given problem accurately.
O 0 =n +4.5 ≥ 38.9, where n is equal to the number.
Incorrect. This equation is not correct as it does not reflect the given problem accurately.
O In +4.5 = 38.9, where n is equal to the number.
Incorrect. This equation is not correct as it does not reflect the given problem accurately.
O In + 4.5 < 38.9, where n is equal to the number.
Incorrect. This inequality is not correct as it only represents a less than relationship, not "at most" relationship mentioned in the problem.
Therefore, the correct answer is:
4.5 + (1/3)*n ≤ 38.9, where n is equal to the number.
To solve the inequality §n + 4.6 < 39.1, where n is the number, we can start by subtracting 4.6 from both sides of the inequality:
n < 39.1 - 4.6
Simplifying the right side gives:
n < 34.5
So, the correct answer is:
n < 34.5