2x2 equations

Question

Colombian coffee beans cost $5.50/lb while Peruvian coffee beans cost $4.25/lb. We want to mix the beans together to produce a 40-lb bag costing $4.60/lb. how many pounds of each type of bean should be used?

Answer 1

assume we need x lb of $5.5 beans and y lb of $4.25 beans

 

5.5x + 4.25y = 4.6 * 40 = 184

x+y = 40

x = 40-y

5.5(40-y) + 4.25y = 184

220 - 5.5y + 4.25y = 184

1.25y = 36,     y = 28.8lb

x = 40-y = 11.2lb

Answer 2

Let x = the pounds of Columbian coffee.  Since we want 40 pounds of the blend, the pounds of Peruvian coffee is 40-x.

 

($5.50)*x + ($4.25)*(40-x) = ($4.60)*40

 

5.5x + 170 - 4.25x = 184

 

1.25x = 14

 

11.2 lbs = x (the amount of Columbian Coffee)

 

The amount of Peruvian coffee is 40 - 11.2 = 28.8 lbs