In which of the following sets of numbers are all the numbers solutions to 60g>3×5?
A. 1, 2, and 3
B. 3, 4, and 5
C. 2, 3, and 4
D. 4, 5, and 6
We can simplify the inequality by dividing both sides by 3:
$$\frac{60g}{3}>5$$
Simplifying further:
$$20g>5$$
Dividing both sides by 20:
$$g>\frac{1}{4}$$
Now we can check each set of numbers:
A. None of these numbers are greater than $\frac{1}{4}$, so none of them satisfy the inequality.
B. All of these numbers are greater than $\frac{1}{4}$, so they all satisfy the inequality.
C. Two of these numbers are greater than $\frac{1}{4}$ (3 and 4), but 2 is not, so only two of them satisfy the inequality.
D. All of these numbers are greater than $\frac{1}{4}$, so they all satisfy the inequality.
Therefore, the set of numbers in which all the numbers satisfy the inequality is $\boxed{\textbf{(B)}\ 3, 4, \text{ and }5}$.
To determine which set of numbers are all solutions to the inequality 60g > 3 × 5, we need to solve the inequality and then check each set of numbers to see if they satisfy the inequality.
First, let's solve the inequality:
60g > 3 × 5
Multiply 3 and 5:
60g > 15
Next, divide both sides of the inequality by 60 to isolate g:
g > 15/60
Simplify the right side:
g > 1/4
Now let's check each set of numbers:
A. 1, 2, and 3:
Checking each number individually:
- For g = 1: 1 is greater than 1/4.
- For g = 2: 2 is greater than 1/4.
- For g = 3: 3 is greater than 1/4.
All numbers in set A are solutions to the inequality.
B. 3, 4, and 5:
Checking each number individually:
- For g = 3: 3 is greater than 1/4.
- For g = 4: 4 is greater than 1/4.
- For g = 5: 5 is greater than 1/4.
All numbers in set B are solutions to the inequality.
C. 2, 3, and 4:
Checking each number individually:
- For g = 2: 2 is not greater than 1/4.
- For g = 3: 3 is greater than 1/4.
- For g = 4: 4 is greater than 1/4.
Not all numbers in set C are solutions to the inequality.
D. 4, 5, and 6:
Checking each number individually:
- For g = 4: 4 is greater than 1/4.
- For g = 5: 5 is greater than 1/4.
- For g = 6: 6 is greater than 1/4.
All numbers in set D are solutions to the inequality.
Therefore, the sets of numbers in which all the numbers are solutions to 60g > 3 × 5 are:
A. 1, 2, and 3
B. 3, 4, and 5
D. 4, 5, and 6
To determine which set of numbers are solutions to the inequality 60g > 3 × 5, we can solve for g.
We can rewrite the inequality as:
60g > 15
Next, we divide both sides of the inequality by 60 to isolate g:
g > 15/60
We simplify 15/60 to get:
g > 1/4
Now we can evaluate each set of numbers to see if they satisfy the inequality:
A. 1, 2, and 3: None of these numbers are greater than 1/4. Therefore, this set is not a solution.
B. 3, 4, and 5: All of these numbers are greater than 1/4. Therefore, this set is a solution.
C. 2, 3, and 4: Some of these numbers are greater than 1/4, but not all of them. Therefore, this set is not a solution.
D. 4, 5, and 6: All of these numbers are greater than 1/4. Therefore, this set is a solution.
From the given options, the set of numbers where all the numbers satisfy the inequality 60g > 3 × 5 is:
D. 4, 5, and 6.