A question of quadratic eqn

Question

A shopkeeper mixes two types of items costing 40$ and 50$. If he sells 50 kg of the mixture for 2200$, what may be the quantity of each item?

Answer 1

X+Y = 50 where X and Y are the weights of each type

So then y = 50 - x

 

40x + 50y = 2200  is the cost

 

40x + 50(50 - x) = 2200

 

40x + 2500 - 50x = 2200

 

2500 - 10x = 2200

 

-10x = -300x

 

x=30 <--  30 pounds of the first type

 

y = 20 <-- 20 pounds of the second type

 

30(40) + 20(50) = 1200 + 1000 = 2200