Mixture problems

Question

A mixture of metal power aluminum and iron oxide that has 12% aluminum and another mature that has 45% aluminum powder. How much of each do you need to make together to get 50 kg of thermite which needs to be 25% aluminum powder?

Answer 1

X+Y = 50

0.12x + 0.45y = 0.25(50) = 12.5

0.12x + 0.45( 50 - x) = 12.5

0.12x + 22.5 - 0.45x = 12.5

-0.33x = -10

0.33x = 10

33x = 1000

x = 1000/33 = 30 and 30/99 = 30 and 10/33 = 30.30

y = 19 and 23/33 = 19.69 = 650/33

CHECK:

X * 12% + y * 45% =

1000/33 * 12/100 + 650/33 * 45/100 =

12000/3300 + 29250/3300 =

41250/3300 =

(25/100)(1650/33) =

(35/100)(50)