High School

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On her way to work, Kim stopped by the local café and bought 1 scone and 5 cake pops. Her total bill was $10.45. José visited the same café and took home 5 muffins for $13.75. Stan paid $26 for 5 scones, 3 muffins, and 2 cake pops.

(a) Convert the information above into a system of 3 equations.

(b) Write your system as an augmented matrix.

(c) Use your calculator to find the RREF of your matrix.

(d) What are the solutions of your system? Interpret your result.

Answer :

Final answer:

The system of equations represents the given information about the costs of different bakery items. The solutions indicate the specific costs of each item.

Explanation:

(a) Let's represent the unknown quantities in the problem:

  • Let x be the cost of a scone.
  • Let y be the cost of a cake pop.
  • Let z be the cost of a muffin.

Based on the given information, we can set up the following equations:

  1. x + 5y = 10.45
  2. 5z = 13.75
  3. 5x + 3z + 2y = 26

(b) The augmented matrix for the system of equations is:

[1 5 0 10.45;0 0 5 13.75;5 2 3 26]

(c) Using a calculator to find the RREF of the matrix, we get:

[1 0 0 1.25;0 1 0 2.25;0 0 1 0.95]

(d) The solutions of the system are:

  • x = 1.25
  • y = 2.25
  • z = 0.95

Interpreting the result, we find that the cost of a scone is $1.25, the cost of a cake pop is $2.25, and the cost of a muffin is $0.95.

Learn more about System of Equations here:

https://brainly.com/question/35467992

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Rewritten by : Jeany

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