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?
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.
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.
A2d+3≤15, where d is the number of days.
B3d+2≥15, where d is the number of days.
C3d+2≤15, where d is the number of days.
D2d+3≥15, where d is the number of days.
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.
An≤131.1
Bn≤103.5
Cn≤112.7
Dn≤11.5
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.
An>15
Bn>45
Cn>9.6
Dn>28.8
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.
Aw≥860
Bw≥51.2
Cw≥86
Dw≥8.6
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 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 greater than or equal to 15 , where d is the number of days.
3d+2≤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≤112.7
n less than or equal to 112.7
n≤11.5
n less than or equal to 11.5
n≤131.1
n less than or equal to 131.1
n≤103.5
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>9.6
n greater than 9.6
n>15
n greater than 15
n>45
n greater than 45
n>28.8
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≥860
w greater than or equal to 860
w≥8.6
w greater than or equal to 8.6
w≥51.2
w greater than or equal to 51.2
w≥86
w greater than or equal to 86
1. The correct answer is C: 1/3n + 4.5 ≤ 38.9, where n is equal to the number.
To solve this inequality, subtract 4.5 from both sides:
1/3n ≤ 34.4
Then, multiply both sides by 3 to isolate the variable:
n ≤ 103.2
The possible values for the number are all numbers less than or equal to 103.2.
2. The correct answer is B: 3d + 2 ≥ 15, where d is the number of days.
To solve this inequality, subtract 2 from both sides:
3d ≥ 13
Then, divide both sides by 3 to isolate the variable:
d ≥ 4.33
Since you can't have a fraction of a day, we round up to the nearest whole number. Therefore, after 5 days, the library will be sure it can run the event.
3. The correct answer is C: n ≤ 112.7
To solve this inequality, subtract 4.6 from both sides:
1/3n ≤ 34.5
Then, multiply both sides by 3 to isolate the variable:
n ≤ 103.5
Therefore, the possible values for the number are all numbers less than or equal to 103.5.
4. The correct answer is B: n > 45
To solve this inequality, add 12 to both sides:
4/5n > 36
Then, multiply both sides by 5/4 to isolate the variable:
n > 45
Therefore, the possible values for the number are all numbers greater than 45.
5. The correct answer is C: w ≥ 86
To solve this inequality, subtract 213 from both sides:
10w ≥ 86
Then, divide both sides by 10 to isolate the variable:
w ≥ 8.6
Therefore, Ellie will have enough money saved after 9 weeks or more.