Q. 65 - Precalculus Enhanced with Graphing Utilities

Question

The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of \(13.45. Not knowing that she went to the store, I also went to the same store, purchased two 1 -pound packages of bacon and three cartons of eggs, and paid a total of \)11.45. Now we want to return two 1-pound packages of bacon and two cartons of eggs. How much will be refunded?

Step-by-Step Solution

Answer

$9.96 will be refunded

Step 1: Given information

wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of $13.45. Also I also went to the same store, purchased two 1 -pound packages of bacon and three cartons of eggs, and paid a total of $11.45.

Step 2: Write and solve the equation

Let x be the bacon packaging and y be carton of eggs

The equation are

$$\begin{gathered} 3x+2y=13.45 \left(1\right) \\ 2x+3y=11.45 \left(2\right) \end{gathered}$$

Multiply equation 1 by 3 and equation 2 by 2 and subtract the equations

$9x+6y=40.35+-4x-6y=-22.95x=17.45$

Therefore $x=3.49$

We find the value of y

$$\begin{gathered} 3x+2y=13.45 \\ 3(3.49)+2y=13.45 \\ y=1.49 \end{gathered}$$

We have to return 2 bacon and 2 carton of eggs

Hence 

$$\begin{gathered} 2x+2y \\ 2(3.49)+2(1.49) \\ =9.96 \end{gathered}$$

Step 3: Conclusion

$9.96 will be refunded