To determine how much it will cost Rachel to buy 2 drinks and 2 sandwiches, let's break down the problem step by step.
1. Let's denote the cost of one drink as [tex]\( d \)[/tex] and the cost of one sandwich as [tex]\( s \)[/tex].
2. We are given the following information from the problem:
- Michael bought 2 drinks and 3 sandwiches for [tex]$13.50:
\[
2d + 3s = 13.50
\]
- Tony bought 5 drinks and 6 sandwiches for $[/tex]30.00:
[tex]\[
5d + 6s = 30.00
\][/tex]
3. These two equations form a system of linear equations. We solve this system to find the values of [tex]\( d \)[/tex] and [tex]\( s \)[/tex].
Equation (1): [tex]\( 2d + 3s = 13.50 \)[/tex]
Equation (2): [tex]\( 5d + 6s = 30.00 \)[/tex]
4. From solving these equations, we find that:
[tex]\[
d = 3.00 \quad \text{and} \quad s = 2.50
\][/tex]
5. Now that we know the cost of one drink ([tex]\( d = 3.00 \)[/tex]) and the cost of one sandwich ([tex]\( s = 2.50 \)[/tex]), we can calculate the total cost for Rachel who buys 2 drinks and 2 sandwiches.
6. Calculate Rachel's total cost:
[tex]\[
\text{Total Cost} = 2d + 2s = 2(3.00) + 2(2.50) = 6.00 + 5.00 = 11.00
\][/tex]
7. Therefore, the cost for Rachel to buy 2 drinks and 2 sandwiches is:
[tex]\[
\boxed{11.00}
\][/tex]
So the correct answer is:
B. [tex]$\$[/tex] 11.00$
