Business letter math question

Question

It says we will need 200 pounds of premium South American coffee at $6.98 a pound. We need this order immediately and I understand that you do not have that type of coffee in stock. However, you explained that you could make that mixture of coffee by blending Brazilian coffee that costs $9.20 per pound with Columbian coffee that costs $5.50 per pound. How many pounds of each kind will be used? Full detailed explanation

Answer 1

Let X = pounds of Brazian coffee being used and Y = pounds of Columbian coffee being used. You also know that the total weight has to be 200 pounds. This means that:

X + Y = 200

In the problem statement, we also know that 200 pounds at a price of $6.98 must be equal as X pounds of Brazlian coffee at a price of $9.20 per pounds plus Y pounds of Columbian coffee at a price of $5.50 per pound. This information gives a second equation:

9.20X + 5.50Y = (200)(6.98)

9.20X + 5.50Y = 1396

From here, you can solve the equations using a couple of different methods. The first method is substitution where you solve one of your two equations for the variable of your choice and plug that into the other equation. The second method is using elimination method. It's entirely up to you on what you feel most comfortable doing. For this problem, it would be easier to use substitution method. Solve the first equation for X and that yields:

X = 200 - Y

and when you plug that into the second equation, you should get:

9.20 (200 - Y) + 5.50Y = 1396

The final step is to simply that equation and solve for Y. Once you find what Y is, plug that number back into either of the first two equations to find what X is and you should have your answer!