I have a math sheet for homework and most questions are similar to the following:
Bob is making treat bags for his daughter's birthday party. he decided to use the recipe below for each bag.
1/3 cup peanuts
3/4 cup pretzels
1/5 cup raisins
2/3 cup popcorn
He needs to make to make 6 bags for each friend and 1/2 bag for his two year old. How much of each ingredient will he need to make 6 1/2 bags? How can I solve this problem?
To solve this problem, you can follow these steps:
Step 1: Calculate the total amount of each ingredient needed for one bag.
For one bag:
- Peanuts: 1/3 cup
- Pretzels: 3/4 cup
- Raisins: 1/5 cup
- Popcorn: 2/3 cup
Step 2: Calculate the total amount of each ingredient needed for 6 bags.
Multiply the amount needed for one bag by the number of bags:
- Peanuts: (1/3) cup × 6 bags = 6/3 cups = 2 cups
- Pretzels: (3/4) cup × 6 bags = 18/4 cups = 4.5 cups
- Raisins: (1/5) cup × 6 bags = 6/5 cups = 1.2 cups
- Popcorn: (2/3) cup × 6 bags = 12/3 cups = 4 cups
Step 3: Calculate the amount of each ingredient needed for the additional half bag.
For half a bag, you can calculate half the amount needed for one bag:
- Peanuts: (1/2) × (1/3) cup = 1/6 cup
- Pretzels: (1/2) × (3/4) cup = 3/8 cup
- Raisins: (1/2) × (1/5) cup = 1/10 cup
- Popcorn: (1/2) × (2/3) cup = 1/3 cup
Step 4: Add the amounts calculated from steps 2 and 3 to find the total amount needed for 6 1/2 bags.
- Peanuts: 2 cups + 1/6 cup = 13/6 cups or 2 1/6 cups
- Pretzels: 4.5 cups + 3/8 cup = 39/8 cups or 4 7/8 cups
- Raisins: 1.2 cups + 1/10 cup = 13/10 cups or 1 3/10 cups
- Popcorn: 4 cups + 1/3 cup = 13/3 cups or 4 1/3 cups
Therefore, Bob will need approximately:
- 2 1/6 cups of peanuts
- 4 7/8 cups of pretzels
- 1 3/10 cups of raisins
- 4 1/3 cups of popcorn
to make 6 1/2 bags.
To solve this problem, you need to find out how much of each ingredient is needed to make 6 1/2 bags.
Let's break down the problem step by step:
1. Calculate the amount of each ingredient for one full bag:
- Peanuts: 1/3 cup
- Pretzels: 3/4 cup
- Raisins: 1/5 cup
- Popcorn: 2/3 cup
2. Calculate the amount of each ingredient for 6 full bags:
- Peanuts: (1/3 cup) × 6 = 6/3 cup = 2 cups
- Pretzels: (3/4 cup) × 6 = 18/4 cup = 4.5 cups
- Raisins: (1/5 cup) × 6 = 6/5 cup = 1.2 cups
- Popcorn: (2/3 cup) × 6 = 12/3 cup = 4 cups
3. Calculate the amount of each ingredient for the additional 1/2 bag:
- Peanuts: (1/3 cup) × (1/2 bag) = 1/6 cup
- Pretzels: (3/4 cup) × (1/2 bag) = 3/8 cup
- Raisins: (1/5 cup) × (1/2 bag) = 1/10 cup
- Popcorn: (2/3 cup) × (1/2 bag) = 1/3 cup
4. Add up the amounts for the full bags and the additional 1/2 bag:
- Peanuts: 2 cups + (1/6 cup) = 12/6 cups + 1/6 cup = 13/6 cups
- Pretzels: 4.5 cups + (3/8 cup) = 36/8 cups + 3/8 cup = 39/8 cups
- Raisins: 1.2 cups + (1/10 cup) = 12/10 cups + 1/10 cup = 13/10 cups
- Popcorn: 4 cups + (1/3 cup) = 12/3 cups + 1/3 cup = 13/3 cups
Therefore, Bob will need the following amounts of each ingredient to make 6 1/2 bags:
- Peanuts: 13/6 cups
- Pretzels: 39/8 cups
- Raisins: 13/10 cups
- Popcorn: 13/3 cups
Multiply.
For example:
Peanuts:
1/3 * 6 1/2 = 1/3 * 13/2 = 13/6 = 2 1/6 cups