Question
A 4-column table with 3 rows. Column 1 has entries run, do not run, total. Column 2 is labeled lift weights with entries 40, blank, 65. Column 3 is labeled do not lift weights with entries blank, x, blank. Column 4 is labeled total with entries 75, blank, 120.
Can you determine what number x represents from the information given? Explain how you got your answer.
Can you determine what number x represents from the information given? Explain how you got your answer.
Answers
GPT-4o mini
To find the value of \( x \), we'll analyze the information provided in the table.
We have:
| | Lift Weights | Do Not Lift Weights | Total |
|---------------|--------------|---------------------|-------|
| Run | 40 | | 75 |
| Do Not Run | | x | |
| Total | 65 | | 120 |
1. We know from the "Total" column that the total number of people (regardless of whether they run or lift weights) is 120.
2. The total number of people who "Run" and "Lift Weights" is 75 (first row).
3. The total number of people who "Lift Weights" can be found by adding together the number of people who "Run" and "Lift Weights" (40) and the number of people who "Do Not Run" and "Lift Weights" (which is currently blank).
Now, since we know the overall totals and can derive some more values from them:
### Step 1: Fill in known values
- Total who "Run" is given as 75.
- 1st row indicates that out of those who run, 40 lift weights and the rest (75 - 40 = 35) do not lift weights. Therefore, we can fill in the second row under "Do Not Lift Weights" next to "Run":
| Run | 40 | 35 | 75 |
### Step 2: Confirm remaining totals under Do Not Run
- Now let's look at the total under "Lift Weights." We know that the total number of people who lift weights is given as:
\( 40 + \text{Do Not Run & Lift Weights} = 65 \)
This implies:
\( 40 + \text{(blank entry)} = 65 \)
So:
\( \text{Do Not Run & Lift Weights} = 65 - 40 = 25 \)
### Step 3: Analyze Do Not Run
Now we move to the second row, where we have those who “Do Not Run”:
- The number of people who "Do Not Lift Weights" (x) is given in column 3.
### We know:
- Total people = 120
- Number who "Run" = 75
- Total "Do Not Run" = 120 - 75 = 45
Therefore, all the people who "Do Not Run" are composed of:
- Those who "Lift Weights" = 25
- Those who "Do Not Lift Weights" = \( x \)
### Thus:
25 + x = 45 (total for "Do Not Run")
Hence, we solve for \( x \):
x = 45 - 25 = 20.
Thus, the value of x is 20. Therefore, we can conclude that \( x \) represents 20.
We have:
| | Lift Weights | Do Not Lift Weights | Total |
|---------------|--------------|---------------------|-------|
| Run | 40 | | 75 |
| Do Not Run | | x | |
| Total | 65 | | 120 |
1. We know from the "Total" column that the total number of people (regardless of whether they run or lift weights) is 120.
2. The total number of people who "Run" and "Lift Weights" is 75 (first row).
3. The total number of people who "Lift Weights" can be found by adding together the number of people who "Run" and "Lift Weights" (40) and the number of people who "Do Not Run" and "Lift Weights" (which is currently blank).
Now, since we know the overall totals and can derive some more values from them:
### Step 1: Fill in known values
- Total who "Run" is given as 75.
- 1st row indicates that out of those who run, 40 lift weights and the rest (75 - 40 = 35) do not lift weights. Therefore, we can fill in the second row under "Do Not Lift Weights" next to "Run":
| Run | 40 | 35 | 75 |
### Step 2: Confirm remaining totals under Do Not Run
- Now let's look at the total under "Lift Weights." We know that the total number of people who lift weights is given as:
\( 40 + \text{Do Not Run & Lift Weights} = 65 \)
This implies:
\( 40 + \text{(blank entry)} = 65 \)
So:
\( \text{Do Not Run & Lift Weights} = 65 - 40 = 25 \)
### Step 3: Analyze Do Not Run
Now we move to the second row, where we have those who “Do Not Run”:
- The number of people who "Do Not Lift Weights" (x) is given in column 3.
### We know:
- Total people = 120
- Number who "Run" = 75
- Total "Do Not Run" = 120 - 75 = 45
Therefore, all the people who "Do Not Run" are composed of:
- Those who "Lift Weights" = 25
- Those who "Do Not Lift Weights" = \( x \)
### Thus:
25 + x = 45 (total for "Do Not Run")
Hence, we solve for \( x \):
x = 45 - 25 = 20.
Thus, the value of x is 20. Therefore, we can conclude that \( x \) represents 20.