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Mrs. Barritz is packing food bags for the sick. Because of the special health needs of the people to whom they will be delivered, 15 less than half of the bags will include some diabetic food.

If she wants to use algebra to find out how many bags do not contain diabetic food, which expression below represents that amount?

Let [tex][tex]$b=$[/tex][/tex] number of bags of food.

A. [tex][tex]$\frac{1}{2}(b-15)$[/tex][/tex]

B. [tex][tex]$b-\left(\frac{1}{2}\right) b+15$[/tex][/tex]

C. [tex][tex]$\frac{1}{2}(b+15)$[/tex][/tex]



Answer :

GinnyAnswer
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]

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