Starbucks wants to sell a 10 lb bag of coffee consisting of 3 flavors: vanilla, hazelnut, mocha.

Question

Starbucks wants to sell a 10 lb bag of coffee consisting of 3 flavors: vanilla, hazelnut, mocha.The vanilla sells for $2 per lb; hazelnut for $2.50 per lb; mocha for $3 per lb. the bag will contain equal parts of hazelnut anf mocha flavored coffee. How many of each flavor are in the 10 lb bag if the bag sells for $26?

Answer 1

This is a systems of equations problem, where you're given enough info to write three equations. I'll use three variables, v = vanilla, h = hazelnut, and m = mocha. 

 

We know the price of each flavor, and the cost of the bag

$2v + $2.50h + $3m = $26 

 

We know the weight of the bag is 10lbs

v + h + m = 10

 

and we know the bag contains equal parts of hazelnut and mocha

h = m

 

You can solve by graphing, substitution, or elimination. I'll use substitution since we already have the variable h isolated.

 

Since h = m, I can substitute it into the middle equation, and solve for v,

v + h + m =10

v + m + m =10

v = 10 - 2m

 

Then I'll substitute both into the top equation:

$2v + $2.50h + $3m = $26

$2(10-2m) + $2.50(m) + $3m = $26

solve for m and 

m = 4 lbs.

 

If we have 4 pounds mocha, then we must also have 4lbs hazelnut (since h = m) and if I use the middle equation again 

v + h + m = 10lbs

v + 4 + 4 = 10lbs

then we see we must have 2 lbs of vanilla.