6. a coffee mix is to be made that sells for $2.50 by mixing two types of coffee. the cafe usually packages…

6. a coffee mix is to be made that sells for $2.50 by mixing two types of coffee. the cafe usually packages has 40 ml of guatemalan coffee for a price of $3.00. they want to blend it with the arabica coffee that costs $1.50. how much of the arabica should the cafe mix into the blend?

6. a coffee mix is to be made that sells for $2.50 by mixing two types of coffee. the cafe usually packages has 40 ml of guatemalan coffee for a price of $3.00. they want to blend it with the arabica coffee that costs $1.50. how much of the arabica should the cafe mix into the blend?

Answer

Explanation:

Step1: Set up the equation

Let $x$ be the volume (in mL) of Arabica coffee. The total cost of the blend is the sum of the costs of each type of coffee. The cost - equation is based on the formula: $\text{Cost per unit}\times\text{Volume}$. The total volume of the blend is $(40 + x)$ mL, and the cost per mL of the blend is $$2.50$. The cost of Guatemalan coffee is $3\times40$, and the cost of Arabica coffee is $1.5x$. So, $2.5(40 + x)=3\times40+1.5x$.

Step2: Expand the left - hand side

Expand $2.5(40 + x)$ using the distributive property $a(b + c)=ab+ac$. We get $2.5\times40+2.5x=100 + 2.5x$. So the equation becomes $100 + 2.5x=120+1.5x$.

Step3: Isolate the variable $x$

Subtract $1.5x$ from both sides of the equation: $100 + 2.5x-1.5x=120+1.5x - 1.5x$. This simplifies to $100+x = 120$. Then subtract 100 from both sides: $x=120 - 100$.

Answer:

$20$ mL