Certainly! Let's break down the problem step by step to determine the correct expression for the number of bags that do not contain diabetic food.
1. Understand the problem statement:
- [tex]\( b \)[/tex] represents the total number of bags.
- 15 less than half of the bags will include diabetic food.
2. Formulate the expression for bags containing diabetic food:
- Half of the total number of bags is [tex]\( \frac{1}{2}b \)[/tex].
- 15 less than this half would be [tex]\( \frac{1}{2}b - 15 \)[/tex].
3. Determine the number of bags that do not contain diabetic food:
- The number of bags that do not contain diabetic food would be the total number of bags minus the number of bags that contain diabetic food.
- So, the expression we need to evaluate is [tex]\( b - \left(\frac{1}{2}b - 15\right) \)[/tex].
4. Simplify the expression:
- Distribute the subtraction across the parentheses:
[tex]\[
b - \left(\frac{1}{2}b - 15\right) = b - \frac{1}{2}b + 15
\][/tex]
Therefore, the correct expression representing the number of bags that do not contain diabetic food is:
[tex]\[
b - \left(\frac{1}{2}\right) b + 15
\][/tex]
So the answer is:
[tex]\[
b - \left(\frac{1}{2} \right) b + 15
\][/tex]
