To complete the two-way frequency table, we need to fill in the missing values based on the provided totals.
Let’s represent the missing values as follows:
- The number of Fourth Graders who prefer Salty snacks: \( x \)
- The number of Third Graders who prefer Sweet snacks: \( y \)
We can use the information in the table to set up the following equations based on the totals:
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For Salty snacks: \[ 35 + x = 43 \quad (1) \]
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For Sweet snacks: \[ y + 42 = 57 \quad (2) \]
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For Third Graders: \[ 35 + y = 50 \quad (3) \]
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For Fourth Graders: \[ x + 42 = 50 \quad (4) \]
Now, let's solve these equations step-by-step.
From equation (1): \[ x = 43 - 35 = 8 \]
From equation (2): \[ y = 57 - 42 = 15 \]
Now we check if these values satisfy the other equations.
Substituting \( y \) into equation (3): \[ 35 + 15 = 50 \quad (True) \]
Substituting \( x \) into equation (4): \[ 8 + 42 = 50 \quad (True) \]
The values we found are consistent. Now we can fill in the table:
- Fourth Graders who prefer Salty snacks (x) = 8
- Third Graders who prefer Sweet snacks (y) = 15
Thus, the completed two-way frequency table is:
| Favorite Snack | Third Graders | Fourth Graders | Total | |----------------|----------------|----------------|-------| | Salty | 35 | 8 | 43 | | Sweet | 15 | 42 | 57 | | Total | 50 | 50 | 100 |
So, the missing values are:
- Fourth Graders who prefer Salty snacks: 8
- Third Graders who prefer Sweet snacks: 15