To complete the table with the proportional relationships and equations provided, we first need to establish the unit price (cost per item) for each situation. Once we know the unit price, we can determine which equation matches each scenario.
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38 candy canes for $12.54
Unit price: \( \frac{12.54}{38} \approx 0.33 \)
Matching equation: \( t = 0.33n \) -
233 pencils for $53.59
Unit price: \( \frac{53.59}{233} \approx 0.23 \)
Matching equation: \( t = 0.23n \) -
17 pillows for $17.51
Unit price: \( \frac{17.51}{17} \approx 1.03 \)
Matching equation: \( t = 1.03n \) -
74 beach balls for $40.70
Unit price: \( \frac{40.70}{74} \approx 0.55 \)
Matching equation: \( t = 0.55n \) -
40 jump ropes for $39.20
Unit price: \( \frac{39.20}{40} = 0.98 \)
Matching equation: \( t = 0.98n \) -
59 songs for $56.05
Unit price: \( \frac{56.05}{59} \approx 0.95 \)
Matching equation: \( t = 0.95n \)
Now, we can summarize the matches in the table format:
| Proportional Relationship | Matching Equation | |---------------------------------------------|-------------------| | 38 candy canes for $12.54 | \( t = 0.33n \) | | 233 pencils for $53.59 | \( t = 0.23n \) | | 17 pillows for $17.51 | \( t = 1.03n \) | | 74 beach balls for $40.70 | \( t = 0.55n \) | | 40 jump ropes for $39.20 | \( t = 0.98n \) | | 59 songs for $56.05 | \( t = 0.95n \) |
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