To determine the missing entries in the table, we first need to establish the relationship between the number of puzzles (x) and the total number of pieces (y) and see if it is indeed proportional.
From the data provided:
- When there are 4 puzzles, there are 420 pieces.
- When there are 6 puzzles, there are 630 pieces.
We can find the number of pieces per puzzle in both cases:
-
For 4 puzzles: \[ \frac{420 \text{ pieces}}{4 \text{ puzzles}} = 105 \text{ pieces per puzzle} \]
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For 6 puzzles: \[ \frac{630 \text{ pieces}}{6 \text{ puzzles}} = 105 \text{ pieces per puzzle} \]
This indicates that the relationship is indeed proportional, where each puzzle contains 105 pieces.
Now, we can use this ratio to predict the number of pieces for 8 and 10 puzzles.
For 8 puzzles:
\[ y = 8 \times 105 = 840 \text{ pieces} \]
For 10 puzzles:
\[ y = 10 \times 105 = 1050 \text{ pieces} \]
Now, we can evaluate the possible entries provided:
- 8 puzzles and 800 pieces (not correct, since it should be 840 pieces)
- 8 puzzles and 840 pieces (correct)
- 10 puzzles and 1,000 pieces (not correct, should be 1050 pieces)
- 10 puzzles and 1,200 pieces (not correct)
The correct entries based on our calculations are:
- For 8 puzzles: 840 pieces (correct)
- For 10 puzzles: 1050 pieces (not listed in your options)
Therefore, the only entry that could be the missing entry in the table is:
- 8 puzzles and 840 pieces.
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