To compare the amount of fruit in each bag, let's first analyze the ratios and calculate the quantities of fruit and nuts based on the specified ratios for both bags.
First Bag:
- Ratio of fruit to nuts: 3:5
- Total pieces: 60
Let the amount of fruit be \(3x\) and the amount of nuts be \(5x\). Therefore, we can set up the equation: \[ 3x + 5x = 60 \] \[ 8x = 60 \] \[ x = 7.5 \]
Now calculating the amounts:
- Fruit: \(3x = 3 \times 7.5 = 22.5\)
- Nuts: \(5x = 5 \times 7.5 = 37.5\)
Second Bag:
- Ratio of fruit to nuts: 7:10
- Total pieces: 60
Let the amount of fruit be \(7y\) and the amount of nuts be \(10y\). Therefore, we can set up the equation: \[ 7y + 10y = 60 \] \[ 17y = 60 \] \[ y \approx 3.5294 \]
Now calculating the amounts:
- Fruit: \(7y = 7 \times 3.5294 \approx 24.69\)
- Nuts: \(10y = 10 \times 3.5294 \approx 35.29\)
Comparison:
- First Bag: \(22.5\) pieces of fruit
- Second Bag: \(24.69\) pieces of fruit
Conclusion:
The second bag has more fruit than the first bag.
Thus, the correct answer is: The second bag, because the ratio is greater.
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