To estimate how much heavier Ari's bag is compared to Juan's bag, we can start with the weights given:
- Juan's bag of apples: \(\frac{31}{7}\) pounds
- Ari's bag of oranges: \(\frac{19}{3}\) pounds
First, we can convert these fractions to mixed numbers to make them easier to estimate.
-
For Juan’s bag: \(\frac{31}{7}\) can be converted to a mixed number: \[ 31 \div 7 = 4 \quad \text{(remainder 3)} \] So, \(\frac{31}{7} = 4 \frac{3}{7}\) which is approximately 4.5 pounds.
-
For Ari’s bag: \(\frac{19}{3}\) can be converted to a mixed number: \[ 19 \div 3 = 6 \quad \text{(remainder 1)} \] So, \(\frac{19}{3} = 6 \frac{1}{3}\) which is approximately 6.3 pounds.
Now, we can compare the weights:
- Juan’s bag is approximately 4.5 pounds.
- Ari’s bag is approximately 6.3 pounds.
To find the difference: \[ 6.3 - 4.5 = 1.8 \]
This is approximately 1 and one-half pounds, or \(1.5\) pounds.
Therefore, the final answer is: 1 and one-half pounds.