A store mixes Brazillian coffee worth $12 per kg and Venezuelan coffee worth $16 per kg. The mixture is to sell for $14 per kg. Find how much of each should be used to make a 528-kg mixture.

Question

A store mixes Brazillian coffee worth $12 per kg and Venezuelan coffee worth $16 per kg. The mixture is to sell for $14 per kg.  Find how much of each should be used to make a 528-kg mixture.

directrix · Answer

Let B = the number of kg of Brazillian coffee
Let V = the number of kg of Venezuelan coffee

B + V = 528

12B is the amount of money invested in B coffee
16V is the amount of money invested in V coffee

12B + 16 V = 528 ( 14) = 7 392

528 ( 14) is the total money value of 528 kg at $14 each

Solving simultaneously,

B +V = 528
12 B + 16 V - 7 392

Solution by substitution:

B = 528 - V

12 ( 528 - V ) + 16 V = 7 392
6 336 - 12 V + 16 V = 7 392
4V = 1 056
V = 264 kg

Back substituting for V in B = 528 - V yields B = 528 - 264 = 264 kg.

Therefore, B = V = 264 kg.

Here's hoping somebody checks this. :)