A pudding recipe for 50 people calls for 4 cups of sugar. Each bag of sugar contains 6 cups. How many bags of sugar will be needed to make this recipe for 300 people?
A.
8 bags
B.
13 bags
C.
4 bags
D.
24 bags
The correct answer and Explanation is :
To determine how many bags of sugar are needed to make the pudding recipe for 300 people, we’ll need to follow these steps:
- Determine the amount of sugar needed for 300 people:
- The original recipe is for 50 people and uses 4 cups of sugar.
- To find out how much sugar is needed for 300 people, we first need to calculate the amount of sugar per person and then scale it up. [
\text{Sugar per person} = \frac{4 \text{ cups}}{50 \text{ people}} = 0.08 \text{ cups per person}
] Now, multiply this by 300 people: [
\text{Total sugar needed} = 0.08 \text{ cups per person} \times 300 \text{ people} = 24 \text{ cups}
]
- Calculate the number of bags required:
- Each bag of sugar contains 6 cups.
- To find out how many bags are required for 24 cups of sugar, divide the total amount of sugar needed by the amount per bag: [
\text{Number of bags} = \frac{24 \text{ cups}}{6 \text{ cups per bag}} = 4 \text{ bags}
]
So, you would need 4 bags of sugar to make the pudding recipe for 300 people.
Explanation:
When scaling up a recipe, it’s essential to proportionally adjust all the ingredients. In this case, by determining the amount of sugar required for 300 people based on the given ratio, we ensure that the flavor and texture of the pudding remain consistent. By calculating the total cups of sugar needed and dividing by the capacity of each sugar bag, we find that 4 bags are necessary. This approach maintains accuracy and ensures you have enough ingredients to prepare the larger batch of pudding.