The weight of a bag of black beans was 12 pounds. The weight of a bag of green beans was 214 ounces. The beans were mixed and packed into 6 bags. a) What is the weight of the mixed... The weight of a bag of black beans was 12 pounds. The weight of a bag of green beans was 214 ounces. The beans were mixed and packed into 6 bags. a) What is the weight of the mixed beans in each bag in ounces? b) What was the weight of the beans that were not packed?
Understand the Problem
The question asks us to calculate the weight of the mixed beans in each of the 6 bags after mixing black beans (12 pounds) and green beans (214 ounces). A second part to the question asks to calculate the weight of beans that were not packed.
Answer
a. $67.67$ ounces b. $0$ ounces
Answer for screen readers
a. The weight of the mixed beans in each bag is approximately $67.67$ ounces. b. The weight of the beans that were not packed is $0$ ounces.
Steps to Solve
- Convert the weight of black beans to ounces
Since 1 pound is equal to 16 ounces, we convert 12 pounds to ounces: $12 \text{ pounds} \times 16 \frac{\text{ounces}}{\text{pound}} = 192 \text{ ounces}$.
- Calculate the total weight of the mixed beans in ounces
The weight of the green beans is already given in ounces (214 ounces). Add the weight of the black beans (in ounces) to the weight of the green beans to find the total weight: $192 \text{ ounces} + 214 \text{ ounces} = 406 \text{ ounces}$.
- Calculate the weight of the mixed beans in each bag
Divide the total weight of the mixed beans by the number of bags (6) to find the weight of the mixed beans in each bag: $\frac{406 \text{ ounces}}{6 \text{ bags}} = 67.666... \text{ ounces per bag}$. Round to $67.67$ ounces.
- Calculate the total packed weight
Multiply the weight of the mixed beans in each bag by the number of bags to find the total packed weight. $6 \text{ bags} \times 67.666... \text{ ounces per bag} = 406 \text{ ounces}$
- Calculate the weight of the beans that were not packed
Since the total amount of mixed beans was 406 ounces, and the total packed weight was 406 ounces, the amount of beans that were not packed would be:
$406 \text{ ounces} - 406 \text{ ounces} = 0 \text{ ounces}$
a. The weight of the mixed beans in each bag is approximately $67.67$ ounces. b. The weight of the beans that were not packed is $0$ ounces.
More Information
The beans were fully packed in the 6 bags.
Tips
A common mistake is forgetting to convert the weight of the black beans from pounds to ounces before adding it to the weight of the green beans. Another mistake is incorrectly performing the division in step 3 or rounding incorrectly.
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