Question

a coffee company wants a new flavor of cajun coffee. how many pounds of coffee worth $10 a pound should be added to 20 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound? (type an integer, proper fraction, or mixed number)

Explanation:

Step1: Set up the equation

Let $x$ be the number of pounds of coffee worth $\$10$ a pound. The value of the $\$3$ - per - pound coffee is $3\times20 = 60$ dollars. The value of the $\$10$ - per - pound coffee is $10x$ dollars. The total weight of the mixture is $(20 + x)$ pounds and its value is $5(20 + x)$ dollars. So, $60+10x=5(20 + x)$.

Step2: Expand the right - hand side

Expand $5(20 + x)$ to get $100 + 5x$. So the equation becomes $60+10x=100 + 5x$.

Step3: Move the $x$ terms to one side

Subtract $5x$ from both sides: $60+10x-5x=100 + 5x-5x$, which simplifies to $60 + 5x=100$.

Step4: Solve for $x$

Subtract 60 from both sides: $5x=100 - 60$, so $5x=40$. Then divide both sides by 5: $x=\frac{40}{5}=8$.

Answer:

8