Given the items and their respective prices, let's find the total cost for 2 burritos, 8 tacos, and 4 chalupas step-by-step.
1. Cost of 2 Burritos:
- The cost of one burrito is [tex]\( b \)[/tex] dollars.
- Therefore, the cost of 2 burritos is [tex]\( 2 \times b = 2b \)[/tex] dollars.
2. Cost of 8 Tacos:
- Each taco costs half the price of a burrito.
- Hence, the cost of one taco is [tex]\( \frac{b}{2} \)[/tex] dollars.
- Therefore, the cost of 8 tacos is [tex]\( 8 \times \frac{b}{2} \)[/tex].
3. Cost of 4 Chalupas:
- Each chalupa costs [tex]\( \text{b} + 0.75 \)[/tex] dollars, where [tex]\( 0.75 \)[/tex] dollars is added to the price of a burrito.
- Hence, the cost of 4 chalupas is [tex]\( 4 \times (b + 0.75) \)[/tex].
Now, we combine all these costs to get the total cost:
[tex]\[ \text{Total cost} = (2b) + (8 \times \frac{b}{2}) + (4 \times (b + 0.75)) \][/tex]
Simplify this expression step-by-step:
- First, simplify the expression for the tacos:
[tex]\[ 8 \times \frac{b}{2} = 4b \][/tex]
- Next, expand the expression for the chalupas:
[tex]\[ 4 \times (b + 0.75) = 4b + 3 \][/tex]
So, the expression for the total cost is:
[tex]\[ 2b + 4b + 4b + 3 \][/tex]
Combine like terms:
[tex]\[ 2b + 4b + 4b + 3 = 10b + 3 \][/tex]
Thus, the given expression matches the first answer choice:
[tex]\[ 2 b + 8 \cdot \frac{b}{2} + 4(b + 0.75) \][/tex]
Evaluating this expression based on [tex]\( b = 1 \)[/tex] dollar, we get the numerical result [tex]\( 13 \)[/tex] dollars, confirming our work.
Therefore, the correct choice is: [tex]\[ 2 b + 8 \cdot \frac{b}{2} + 4(b + 0.75) \][/tex]
