Question

Customer 1 buys 2 hamburgers and 4 drinks, and his total is $13.00. Customer 2 buys 3 hamburgers and 7 drinks, and his total comes out as $21.00. PART A. You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?PART B. Show your work or explain how you got your answer.

Answer 1

Answer:

$\text{Total= \ 43.5}$

Step by step explanation:

To solve this situation we can create a system of linear equations, with the given information for the customers:

Let x be the price for each hamburger

Let y be the price for each drink

$\begin{gathered} 2x+4y=13\text{ (1)} \\ 3x+7y=21\text{ (2)} \end{gathered}$

To solve for x and y. We can use the substitution method, which consists of isolating one variable in one of the equations and substitute it into the other.

Let's isolate y in (1):

$\begin{gathered} 4y=13-2x \\ y=\frac{13}{4}-\frac{2}{4}x \end{gathered}$

Now, substitute it into equation (2).

$3x+7(\frac{13}{4}-\frac{2}{4}x)=21$

Solve for x:

$\begin{gathered} 3x+\frac{91}{4}-\frac{7}{2}x=21 \\ -\frac{1}{2}x+\frac{91}{4}=21 \\ -\frac{1}{2}x=21-\frac{91}{4} \\ -\frac{1}{2}x=-\frac{7}{4} \\ x=\frac{7\cdot2}{4} \\ x=\frac{7}{2}=\text{ \ 3.5 } \end{gathered}$

With the x-value, we can substitute it into the equation (1) to find the price for each drink:

$\begin{gathered} y=\frac{13}{4}-\frac{2}{4}(3.5) \\ y=\frac{13}{4}-\frac{7}{4} \\ y=\frac{6}{4}=\text{ \ 1.5} \end{gathered}$

Therefore, the price for each hamburger is $3.5 and for each drink is $1.5.

Now, if we want to buy 8 drinks and 9 hamburgers:

$\begin{gathered} \text{Total}=(8\cdot1.5)+(9\cdot3.5) \\ \text{Total}=12+31.5 \\ \text{Total= \ 43.5} \end{gathered}$