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    mgsecond powder    mg

Question
Asked Oct 12, 2019

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
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Expert Answer

Step 1

Given:

 Powder-1: 20% vitamin B1 and 30% vitamin B2

 Powder-2 : 15% vitamin B1 and 10% vitamin B2.

Required mixture:

140 mg of vitamin B1 and 190 mg of vitamin B2

Step 2

Say, the mass of  powder-1 needed is x and mass of powder-2 is y

So,

Mass of vitamin B1 :

(0.20 x + 0.15 y = 140 mg ) ----------------equation.1

Mass of vitamin B2:

(0.30 x + 0.1y = 190 mg) ---------------------equation.2

Multiply equation 1 with 3 and equation 2 with 2.

      (0.20 x + 0.15 y = 140 mg ) X 3

                                     = 0.6 x + 0.45y = 420--------------------equation.3

      (0.30 x + 0.1y = 190 mg)  X 2  

                                     = 0.6x + 0.2y = 380 -----------------------equation.4

Subtract equation 4 from 3,

0.6 x + 0.45y = 420

0.6x + 0.2y = 380

-----------------------------------

0.25 y = 40

  Y = 160

Step 3

Substitute the y value in equation 1

0.20 x + 0.15 X 160 = 140 mg

0.20 x + 24 = ...

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