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Review Questions - TSI Test

1. Michael bought 2 drinks and 3 sandwiches for [tex]$\$[/tex] 13.50[tex]$. Tony bought 5 drinks and 6 sandwiches for $[/tex]\[tex]$ 30$[/tex]. If Rachel buys 2 drinks and 2 sandwiches, how much will it cost her?

A. [tex]$\$[/tex] 7.50[tex]$
B. $[/tex]\[tex]$ 11.00$[/tex]
C. [tex]$\$[/tex] 11.50[tex]$
D. $[/tex]\[tex]$ 6.50$[/tex]


Sagot :

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]$\$[/tex] 11.00$
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