2.5.4 Solving Systems of Equations Using Real-World Examples

Algebra 12.5.4 Solving Systems of Equations Using Real-World Examples

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On a family outing, Marlon bought 5 cups of hot cocoa and 4 pretzels for $18.40. Some of his family members would like a second serving, so he went back to the same food stand and bought another 2 cups of hot cocoa and 4 pretzels for $11.20.

Here is a system of equations that represent the quantities and constraints in this situation.

${\begin{matrix} 5 c + 4 p = 18.40 \\ 2 c + 4 p = 11.20 \end{matrix}$

What does the solution to the system, $(c, p)$ , represent in this situation?

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The values of $c$ and $p$ represent the price of a cup of hot cocoa and the price of a pretzel that Marlon bought.

If we add the second equation to the first equation, we have a new equation: $7 c + 8 p = 29.60$ .

Explain why the same $(c, p)$ pair that is a solution to the two original equations is also a solution to this new equation.

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The new equation shows the total number of cups of hot cocoa and total number of pretzels on one side, and the total amount Marlon spent on the other side. The price of each cup of hot cocoa and the price of each pretzel haven’t changed.

Does the equation $7 c + 8 p = 29.60$ help us solve the original system? If you think so, explain how it helps. If you don’t think so, explain why not and what would help us solve the system.

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No, it doesn’t help. For example: It doesn’t eliminate a variable. What would help is subtracting the second equation from the first to get $3 c = 7.20$ . Then we can find $c$ and solve for $p$ .

Video: Solving Systems of Equations Using Real-World Examples

Watch the following video to learn more about when addition is useful for solving systems of equations.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/2-5-4-solving-systems-of-equations-using-real-world-examples

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