Question

at Kami Export-Genel To-do 8. A coffee shop sells special blend of coffee that comes in a 100 pound bag and costs $3.50 per pound. It is a mix of coffee from Costa Rica at $4 per pound and Columbian at $3 per pound. Find the amounts of each type of coffee used to make the mix. (Hint: Find the total cost of the coffee mix)

Answer 1

EXPLANATION

Let's see the facts:

Bag weight = 100 pound

Cost = 3.5/pound

Mix-->

Costa Rica Columbian

4/pound 3/pound

Let's call x to the amount of coffee from Costa Rica and y to the amount of coffee from Columbian, the equation would be:

Bag= x + y = 100

Isolating y:

y= 100 - x

We also want to sell it for $3.5

`(4x+3y)/(x+y)=3.5`

Substituting terms:

`\frac{4x\text{ + 3y}}{100}=3.5`

Multiplying both sides by 100:

`4x\text{ + 3y = 3.5}\cdot100`

Applying the distributive property:

4x + 3y = 350

Substituting y=100 - x on it:

4x + 3(100-x) = 350

Applying the distributive property:

4x + 300 -3x = 350

Grouping and adding like terms:

x + 300 = 350

Subtracting -300 to both sides:

x = 350 - 300

Subtracting numbers:

x = 50

Now, we need to find the y-value applying the first equation:

y= 100 - 50 = 50

Answers: The amount of Costa Rica coffee is 50 pounds and the amount of Columbian coffee is 50 pounds.