Question

A pharmacist has two vitamin-supplement powders. The first powder is 10% vitamin B1 and 30% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each powder should the pharmacist use to make a mixture that contains 80 mg of vitamin B1 and 200 mg of vitamin B2?

Answer 1

`560` mg of powder 1 and
`160` mg of powder 2

Step-by-step explanation:

Let "X" denotes weight of powder 1 added to the new mixture and "Y" denotes weight of powder 2 added to the new mixture

Total weight of vitamin B1 in the mixture is equal to
`80` mg

Total weight of vitamin B2 in the mixture is equal to
`200` mg

Equation 1

`0.1 X + 0.15 Y= 80`

Equation 2

`0.3 X + 0.2 Y= 200`

Let us simplify the above two equations, we will get

`10 X + 15 Y = 8000\\3X + 2Y = 2000`

`2 (10 X + 15 Y = 8000), 20X + 30 Y = 1600015(3X + 2Y = 2000), 45X +30Y = 30000\\25 X = 14000\\X = 560`

Substituting value of X in equation 2 we get

`0.3 * 560 + 0.2 Y = 200\\0.2 Y = 200 - 168\\Y = 160`