A trail mix recipe calls for 1 3.4 cups of raisins, The recipe requires 3/8 cup less pecans than raisins and 7/8 cup more granola than raisins. How many cups of ingredients are in this raisin?

Let's solve the problem step by step:

1. **Amount of raisins:**  
   The recipe calls for \(1 \frac{3}{4}\) cups of raisins. Convert this to an improper fraction:
   \[
   1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} \text{ cups}
   \]

2. **Amount of pecans:**  
   The recipe requires \( \frac{3}{8} \) cup less pecans than raisins. So, subtract \( \frac{3}{8} \) from \( \frac{7}{4} \):
   \[
   \text{Pecans} = \frac{7}{4} - \frac{3}{8}
   \]
   To subtract these, find a common denominator:
   \[
   \frac{7}{4} = \frac{14}{8}, \quad \text{so } \frac{14}{8} - \frac{3}{8} = \frac{11}{8} \text{ cups of pecans}
   \]

3. **Amount of granola:**  
   The recipe requires \( \frac{7}{8} \) cup more granola than raisins. So, add \( \frac{7}{8} \) to \( \frac{7}{4} \):
   \[
   \text{Granola} = \frac{7}{4} + \frac{7}{8}
   \]
   Again, find a common denominator:
   \[
   \frac{7}{4} = \frac{14}{8}, \quad \text{so } \frac{14}{8} + \frac{7}{8} = \frac{21}{8} \text{ cups of granola}
   \]

4. **Total amount of ingredients:**  
   Add the amounts of raisins, pecans, and granola together:
   \[
   \text{Total} = \frac{7}{4} + \frac{11}{8} + \frac{21}{8}
   \]
   Convert \( \frac{7}{4} \) to have the same denominator as the other fractions:
   \[
   \frac{7}{4} = \frac{14}{8}
   \]
   Now add them:
   \[
   \frac{14}{8} + \frac{11}{8} + \frac{21}{8} = \frac{46}{8} = \frac{23}{4} \text{ cups}
   \]

   Simplify \( \frac{23}{4} \) to a mixed number:
   \[
   \frac{23}{4} = 5 \frac{3}{4} \text{ cups}
   \]

So, the total amount of ingredients in the trail mix is \( 5 \frac{3}{4} \) cups.

Would you like more details on any part of this solution? 

Here are some related questions:

1. How would the total amount change if the recipe used double the amount of raisins?
2. What if the recipe required 1 cup more granola instead of \( \frac{7}{8} \) cup more?
3. How many cups of ingredients would be needed if the recipe used \( \frac{5}{4} \) cups of raisins instead?
4. What is the total if the amount of pecans required was instead \( \frac{5}{8} \) cup less than the raisins?
5. How many total cups of ingredients would be used if \( \frac{1}{2} \) cup of chocolate chips were added to the mix?

**Tip:** When working with fractions, finding a common denominator can help simplify adding or subtracting them.

Learn how to solve a trail mix recipe problem involving raisins, pecans, and granola. This math problem covers fractions and arithmetic operations. Find out the amount of each ingredient required based on the given ratios. Suitable for students in Grades 5-6.

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