A culinary club earns $1,360 from a dinner service. They sold 45 adult meals and 80 student...

Question:

A culinary club earns $1,360 from a dinner service. They sold 45 adult meals and 80 student meals. An adult meal costs twice as much as a student meal. What is the cost of an adult meal?

Consistent System of Equations:

When it comes to linear equations there are two instances when a system of linear equations are consistent. It is when the lines intersect each other at a unique point and when the lines are coincident.

Answer and Explanation:

The club earns $1,360 selling 45 adult meals and 80 student meals. Let {eq}x {/eq} stand for the cost of a student meal and {eq}2x {/eq} for the cost of an adult meal. The equation for the amount involved for all the meals would be:

{eq}80x + 45(2x) = 1360 {/eq}

Solving for {eq}x {/eq}:

{eq}\begin{align} 80x + 45(2x) &= 1360 \\ 80x + 90x &= 1360 \\ 170x &= 1360 \\ \dfrac {170x}{170} &= \dfrac{1360}{170} \\ x &= 8 \end{align} {/eq}

Since the adult meal is twice the amount of the student meal:

{eq}2x = 2(8) = 16 {/eq}

The cost of an adult meal is $16.00.


Learn more about this topic:

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Consistent System of Equations: Definition & Examples

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 8
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