World problem

Question

Kley work at a donut factory, we're a 10-oz of coffee cost 95¢, a 14-oz cost 1.15$ and 20-oz cup cost 1.50$. During one busy period Kyle secure 59 cups of coffee, using 548 once of coffee, while collecting a total of 47.40$.How many cups did fill?

Answer 1

Let x = number of 10-ounce cups sold at 95 cents.

Let y = number of 14-ounce cups sold at 115 cents

Let z = number of 20-ounce cups sold at 150 cents

x + y + z = 59

10x + 14y + 20z = 548

95x + 115y + 150z = 4740

We are asked how many cups were filled. That's easy, x + y + z = 59.

However, there is enough information provided to tell how many cups of each size were filled.

Let A be the matrix of coefficients:

1 1 1

10 14 20

95 115 150

Let b represent the vector of the unknowns:

[ x, y, z ]

Let c represent the vector of numbers on the Right Hand Side of the equal signs:

59

548

4740

Then the matrix equation to solve is

Ab = c

To solve for b, I used Octave, a free online advanced math system and it came up with b =

x = -127.00

y = 317.00

z = -131.00

Obviously, there can be no negative answers, so there must be a mistake in the problem statement.