The grocery store we use does not mark prices on its goods M

The grocery store we use does not mark prices on its goods. My wife went to this store, bought four packages of bacon and five cartons of eggs, and paid a total of dollar 17.41. Not knowing that she went to the store, I also went to the same store, purchased five packages of bacon and four cartons of eggs, and paid a total of dollar 18.41. Now we want to return four packages of bacon and four cartons of eggs. How much will be refunded? How much will we be refunded? dollar

Solution

Now, on multiplying the 1^st equation by 5 and the 2^nd equation by 4, we get 20x +25y = 87.05…(3) and 20x +16y = 73.64…(4). Further, on subtracting the 4^th equation from the 3^rd equation, we get 20x+25y-20x-16y = 87.05-73.64 or, 9y = 13.41 so that y = 13.41/9 = 1.49. Then, on substituting y = 1.49 in the 1^st equation, we get 4x+5*1.49 = 17.41 or, 4x= 17.41-7.45 = 9.96 so that x = 9.96/4 = 2.49. Thus, the price of 1 package of bacon is $ 2.49 and the price of 1 carton of eggs is $ 1.49. Therefore, the price of 4 packages of bacon is $ 2.49*4 = 9.96 and the price of 4 cartons of eggs is $ 1.49*4 = $ 5.96. Hence, on returning 4 packages of bacon and 4 cartons of eggs, the refund will be $ 9.96+$ 5.96 = $ 15.92.