Solving a percent mixture problem using a system of linear equations

Question

A mixture of two powdered substances contains 20% of substance A by mass and 10% of substance B. How much of each must be added to 50 kg of this mixture in order to produde a new mixture containing 25% of substance A and 15% of substance B?

Answer 1

20% A, 10% B, 50kg

25%A, 15%B, 50kg + xA +yB?

20 to 30% and 10 to 15% = 50 +25 = 75 kg

each is increased by 50%

with 12.5 kg of each A and B

for 20 to 25%, half as much A is added or 12.5/2 = 6.25 kg

add 6.25 kg of A and 12.5 kg of B to get 50+12.5+6.25 = 78.75 kg where A is 25% and B is 15%

40% is A and B = .4(78.75) = 31.5 kg A and B

60% is not A or B = 47.25 kg

originally 30% was A and B =.3(50) = 15 kg

with 70% not A or B = 35 kg