The sum of 11 and three-fourths of a number is less than 112. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as the variable, and write the inequality so that the x term comes first. Where necessary, write numbers as fractions (rather than decimals). Do not solve the inequality.
Let's say the number is x.
The sum of 11 and three-fourths of a number is written as 11 + (3/4)x.
According to the problem, this sum is less than 112, so the inequality is:
11 + (3/4)x < 112
Grace will receive $50 plus $5 per child for babysitting this afternoon. She is
hoping to make at least $63 to buy a new video game tonight. How many children does she need to babysit? Write an inequality that could be used to solve this problem. Use the letter x as the variable. Do not solve the inequality.
Let's say the number of children Grace needs to babysit is x.
She will earn $5 per child, so she will earn 5x dollars.
Including the initial $50, her total earnings will be $50 + 5x.
According to the problem, she wants to make at least $63, so the inequality is:
50 + 5x ≥ 63
Ten less than twice a number is equal to at most 52. What are all the possible values of the number? Inuk wrote the inequality 2x - 10 ≤ 52, where x equals the number, to help solve this problem. Solve his inequality.
Use the letter x as your variable and write your x term first.
To solve the inequality 2x - 10 ≤ 52, we want to isolate x on one side of the inequality.
First, we add 10 to both sides of the inequality:
2x - 10 + 10 ≤ 52 + 10
2x ≤ 62
Next, we divide both sides of the inequality by 2 to isolate x:
(2x)/2 ≤ 62/2
x ≤ 31
Therefore, the solution to the inequality is x ≤ 31.
The possible values for the number that satisfy the inequality are all values less than or equal to 31.
Helena will receive &53 plus $4 per kid for babysitting this afternoon. She is
hoping to make at least $69. How many kids does she need to babysit? She writes the inequality 4x + 53 > 69, where x equals the number of kids, to help figure this out. Solve her inequality. Use the letter x as your variable and write your x term first.
To solve the inequality 4x + 53 > 69, we want to isolate x on one side of the inequality.
First, we subtract 53 from both sides of the inequality:
4x + 53 - 53 > 69 - 53
4x > 16
Next, we divide both sides of the inequality by 4 to isolate x:
(4x)/4 > 16/4
x > 4
Therefore, the solution to the inequality is x > 4.
To make at least $69, Helena needs to babysit more than 4 kids.
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)
O1/3n + 4.5 ≤ 38.9, where n is equal to the number.
O 4.5 + 1/3 + n ≤ 38.9, where n is equal to the number.
O1/3n+ 4.5=38.9, where n is equal to the number.
O1/3n + 4.5 ≥ 38.9, where n is equal to the number.
The correct inequality that could be used to solve this problem is:
(1/3)n + 4.5 ≤ 38.9, where n is equal to the number.
To solve this inequality, we can subtract 4.5 from both sides:
(1/3)n ≤ 38.9 - 4.5
(1/3)n ≤ 34.4
Then, we can multiply both sides by 3/1 to isolate n:
3/1 * (1/3)n ≤ 3/1 * 34.4
n ≤ 103.2
Therefore, the possible values of the number are all numbers less than or equal to 103.2.
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. (1 point)
• 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.
O2d+3 > 15, where d is the number of days.