word problem

Question

A store mixes Brazilian coffee worth $12 per kilogram and Venezuelan coffee worth $14 per kilogram.the mixture is to sell for 13 dollars per kilogram. Find how much of each should be used to make a 216 kilogram mixture.

Answer 1

b=number of pounds of the $12 Brazilian bean needed

v=number of pounds of the $14 Venezuelan bean needed

 

You have two variables, so you need two equations:

Equation 1: b+v=216 (because the mixture has a total of 216 pounds)

Equation 2: 12b + 14v = (13)*216 (each quantity is cost per pound *number of pounds)

Isolate for b in Equation 1: b = 216-v, and substitute into Equation 2:


12(216-v) + 14v = (13)*216

2592-12v+14v=2808

2592+2v=2808

2v=2808-2592

2v=216

v=108

 

So you need 108 pounds of Venezuelan coffee.  To find how much Brazilian coffee, plug 108 (which is v) into the original equation and solve for b.

 

b+v=216

b+108=216

b=216-108

b=108

So you would need 108 pounds each of Brazilian and Venezuelan coffee.

 

CHECK:

 

12b + 14v = (13)*216  (Second equation -- plug in 108 for b and 108 for v.  Solve.)

12(108)+14(108)=13(216)

1296+1512=2808

2808=2808