(Question 1) 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
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 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.
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.
(Question 2) 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
13n+4.5=38.9, where n is equal to the number.
Start Fraction 1 over 3 end fraction n plus 4.5 equals 38.9 , where n is equal to the number.
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 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.
(Question 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 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≤112.7
n less than or equal to 112.7
n≤11.5
n less than or equal to 11.5
n≤131.1
(Question 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 45n−12>24, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses
n>28.8
n greater than 28.8
n>45
n greater than 45
n>15
n greater than 15
n>9.6
(Question 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 point)
Responses
w≥86
w greater than or equal to 86
w≥51.2
w greater than or equal to 51.2
w≥860
w greater than or equal to 860
w≥8.6
Question 1:
To solve this problem we can create an inequality. We know that there are already 3 people signed up and each day 2 more sign up. Let d be the number of days after which the total number of people signed up reaches at least 15.
So, the inequality will be:
3 (current sign-ups) + 2d (additional sign-ups over d days) ≥ 15
The correct expression is:
2d + 3 ≥ 15, where d is the number of days.
Question 2:
To translate the given information into an inequality, let n be the number. According to the problem, 4.5 plus one-third of the number should be at most 38.9, which implies:
4.5 + (1/3)n ≤ 38.9
To express it using characters from the given choices, this would be:
(1/3)n + 4.5 ≤ 38.9, where n is equal to the number.
Question 3:
Artem wrote the inequality as 1/3n + 4.6 ≤ 39.1, which appears to be a mistake since the fraction should be 1/3 and not 13. Assuming that it was a typographical error, the correct inequality should be:
(1/3)n + 4.6 ≤ 39.1
Now, solving for n:
(1/3)n ≤ 39.1 - 4.6
(1/3)n ≤ 34.5
n ≤ 34.5 * 3
n ≤ 103.5
So the answer is n ≤ 103.5.
Question 4:
Lucia's inequality should represent four-fifths of a number, so using the correct fraction, the inequality should be:
(4/5)n - 12 > 24
Let's correct the expression and solve the inequality:
(4/5)n > 24 + 12
(4/5)n > 36
n > 36 * (5/4)
n > 45
So the answer is n > 45.
Question 5:
Ellie's inequality is 10w + 213 ≥ 299. Let's solve for w:
10w ≥ 299 - 213
10w ≥ 86
w ≥ 86 / 10
w ≥ 8.6
Ellie would need to sav for at least 9 weeks (since we're working with whole weeks, we would round up from 8.6). Thus, the answer is w ≥ 8.6.
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 45n−12>24, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses
n>28.8
n greater than 28.8
n>45
n greater than 45
n>15
n greater than 15
n>9.6
Let's correct Lucia's inequality and solve the correct version. The phrase "Twelve less than four-fifths of a number is more than 24" translates to the inequality:
(4/5)n - 12 > 24
This inequality implies that when you take four-fifths of a number n, and then subtract 12 from it, the result should be greater than 24. Lucia incorrectly wrote the inequality as 45n - 12 > 24, which is not equivalent to the original statement.
Now let's solve the correct inequality:
(4/5)n - 12 > 24
(4/5)n > 24 + 12
(4/5)n > 36
Now we'll multiply both sides by the reciprocal of (4/5), which is (5/4):
n > 36 * (5/4)
n > 45
So the answer is n > 45.
For Question 1, 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. We need to determine after how many days will the library be sure it can run the event.
We can represent the number of days as the variable d. Since the library expects 2 more people to sign up each day, we can multiply 2 by the number of days and add it to the initial number of people signed up (3). The inequality to represent this situation is:
3d + 2 ≥ 15
Thus, the correct response is: 3d+2≥15, where d is the number of days.
For Question 2, the problem states that the sum of 4.5 and one-third of a number is at most 38.9. To solve for the possible values of the number, we need to write an inequality.
Let's represent the number as the variable n. The sum of 4.5 and one-third of the number can be written as:
4.5 + 1/3n
The inequality to represent this situation is:
4.5 + 1/3n ≤ 38.9
Thus, the correct response is: 4.5+13+n≤38.9, where n is equal to the number.
For Question 3, the problem states that the sum of 4.6 and one-third of a number is at most 39.1. We are given the inequality 13n + 4.6 ≤ 39.1, where n is the number. We need to solve this inequality to find the possible values of the number.
To solve for n, we can subtract 4.6 from both sides of the inequality:
13n ≤ 39.1 - 4.6
This simplifies to:
13n ≤ 34.5
Dividing both sides of the inequality by 13 gives us:
n ≤ 34.5 / 13
Thus, the correct response is: n≤2.65
For Question 4, the problem states that twelve less than four-fifths of a number is more than 24. We are given the inequality 45n−12>24, where n is the number. We need to solve this inequality to find the possible values of the number.
To solve for n, we can add 12 to both sides of the inequality:
45n > 24 + 12
This simplifies to:
45n > 36
Dividing both sides of the inequality by 45 gives us:
n > 0.8
Thus, the correct response is: n>0.8
For Question 5, Ellie wants to have at least $299 saved before buying a phone. She currently has $213 saved and receives $10 a week as an allowance. We need to determine after how many weeks Ellie will have enough money saved.
Let's represent the number of weeks as the variable w. To calculate the total amount of money Ellie will have after w weeks, we can multiply her allowance ($10) by the number of weeks and add her initial savings ($213). The inequality to represent this situation is:
10w + 213 ≥ 299
Thus, the correct response is: 10w+213≥299, where w is the number of weeks.