1.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?
2.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.
3.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.
4.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 4/5n−12>24, where n equals the number, to help solve this problem. Solve her inequality.
5.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. To solve this problem, let's start by defining the unknown number as "x". The sum of 4.5 and one-third of the number is equal to at most 38.9. Mathematically, we can write this as:
4.5 + (1/3)x ≤ 38.9
This inequality states that the sum of 4.5 and one-third of the number is less than or equal to 38.9. To solve for x, we can isolate it by subtracting 4.5 from both sides:
(1/3)x ≤ 38.9 - 4.5
(1/3)x ≤ 34.4
Next, to eliminate the fraction, we can multiply both sides by 3:
3 * (1/3)x ≤ 3 * 34.4
x ≤ 103.2
Therefore, all possible values of the number are less than or equal to 103.2.
2. The library needs at least 15 people to sign up for an event in order to run it. If 3 people have already signed up and the library expects 2 more people to sign up each day, we can express this situation as an inequality.
Let "d" represent the number of days. The number of people who signed up after "d" days can be represented as:
3 + 2d
To ensure that there are at least 15 people, we can write the inequality:
3 + 2d ≥ 15
Simplifying the inequality, we have:
2d ≥ 15 - 3
2d ≥ 12
To find the number of days needed for the library to be sure it can run the event, we divide both sides of the inequality by 2:
d ≥ 6
Therefore, after 6 or more days, the library can be sure to have enough people to run the event.
3. Artem wrote the inequality 1/3n + 4.6 ≤ 39.1 to solve the problem. Let's solve this inequality. We can start by isolating "n" by subtracting 4.6 from both sides:
1/3n ≤ 39.1 - 4.6
1/3n ≤ 34.5
To eliminate the fraction, we can multiply both sides by 3:
3 * (1/3n) ≤ 3 * 34.5
n ≤ 103.5
Therefore, all possible values of the number (n) are less than or equal to 103.5.
4. Lucia wrote the inequality 4/5n - 12 > 24 to solve the problem. Let's solve this inequality. We can start by isolating "n" by adding 12 to both sides:
4/5n > 24 + 12
4/5n > 36
To eliminate the fraction, we can multiply both sides by 5:
5 * (4/5n) > 5 * 36
4n > 180
Now, to solve for "n", we divide both sides by 4:
n > 180/4
n > 45
Therefore, all possible values of the number (n) are greater than 45.
5. Ellie wrote the inequality 10w + 213 ≥ 299 to figure out how many weeks it will take her to have enough money saved. Let's solve this inequality. We can start by subtracting 213 from both sides:
10w ≥ 299 - 213
10w ≥ 86
To solve for "w", we divide both sides by 10:
w ≥ 86/10
w ≥ 8.6
Therefore, Ellie will have enough money saved in at least 9 weeks or more.