How many mg for first powder and second powder are required to make mixture

Question

A pharmacist has two vitamin-supplement powders. The first powder is 20% vitamin B1 and 30% vitamin B2. The second is 15% vitamin B1 and 10% vitamin B2. How many milligrams of each powder should the pharmacist use to make a mixture that contains 140 mg of vitamin B1 and 190 mg of vitamin B2?
first powder             mg
second powder        mg

Answer 1

x = mg of the 1st powder

y = mg of the 2nd powder

Eq 1:  (x)(0.2) + (y)(0.15) = 140 mg B1

Eq 2:  (x)(0.3) + (y)(0.10) = 190 mg B2

Expanding Eq 1:  0.2x + 0.15y = 140

x + 0.75y = 700

x = 700 - 0.75y

Substituting into Eq 2:

(700 - 0.75y)(0.3) + 0.1y = 190 

y = 160 mg of 2nd powder

 

(x)(0.2) + (160)(0.15) = 140 

x = 580 mg of the 1st powder