To determine the total weight of the mixture, we need to sum the weights of the individual ingredients.
1. Convert the mixed numbers to improper fractions or decimals for easier addition:
- Ingredient A: [tex]\( 3 \frac{2}{4} \)[/tex]
- Convert this to a decimal: [tex]\( 3 + \frac{2}{4} = 3 + 0.5 = 3.5 \)[/tex]
- Ingredient B: [tex]\( 1 \frac{3}{4} \)[/tex]
- Convert this to a decimal: [tex]\( 1 + \frac{3}{4} = 1 + 0.75 = 1.75 \)[/tex]
- Ingredient C: [tex]\( 4 \frac{1}{2} \)[/tex]
- Convert this to a decimal: [tex]\( 4 + \frac{1}{2} = 4 + 0.5 = 4.5 \)[/tex]
2. Add the decimal equivalents of the weights of the ingredients:
- Total weight = Ingredient A + Ingredient B + Ingredient C
- Total weight = [tex]\( 3.5 + 1.75 + 4.5 \)[/tex]
3. Sum the weights:
- [tex]\( 3.5 + 1.75 = 5.25 \)[/tex]
- [tex]\( 5.25 + 4.5 = 9.75 \)[/tex]
Therefore, the total weight of the mixture is [tex]\( 9.75 \)[/tex] pounds, which is equivalent to [tex]\( 9 \frac{3}{4} \)[/tex] pounds.
Thus, the correct answer is:
a. [tex]\( 9 \frac{3}{4} \)[/tex]
