A coffee company wants a new flavor of cajun coffee. How many pounds of coffee worth $7 a pound...

Question:

A coffee company wants a new flavor of cajun coffee. How many pounds of coffee worth $7 a pound should be added to 10 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound?

Multi-Step Linear Equation:

  • A linear equation of one variable is an equation in terms of only one variable of degree 1.
  • The value of the variable which satisfies the equation is called the solution of the equation.
  • A multi-step linear equation is a linear equation that can be solved using multiple algebraic operations on both sides of the equation.

Answer and Explanation:

Let us assume the number of pounds of {eq}\$ 7 {/eq} coffee is {eq}x {/eq}.

This is mixed with {eq}10 {/eq} pounds of {eq}\$ 3 {/eq} coffee.

The result is {eq}(10+x) {/eq} pounds of {eq}\$ 5 {/eq} coffee.

So we get the equation:

$$7(x)+ 3(10) = 5 (x+10)\\[0.4cm] 7x+30 = 5x+50 \\[0.4cm] \text{Subtracting 5x from both sides},\\[0.4cm] 2x+30=50\\[0.4cm] \text{Subtracting 30 from both sides},\\[0.4cm] 2x=20\\[0.4cm] \text{Dividing both sides by 2},\\[0.4cm] x= \color{blue}{\boxed{\mathbf{10 \text{ pounds}}}} $$


Learn more about this topic:

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How to Solve Multi-Step Algebra Equations in Word Problems

from Algebra I: High School

Chapter 8 / Lesson 20
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