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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?

Respuesta :

Answer:

[tex]560[/tex] mg of powder 1 and [tex]160[/tex] mg of powder 2

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 [tex]80[/tex] mg

Total weight of vitamin B2 in the mixture is equal to [tex]200[/tex] mg

Equation 1

[tex]0.1 X + 0.15 Y= 80[/tex]

Equation 2

[tex]0.3 X + 0.2 Y= 200[/tex]

Let us simplify the above two equations, we will get

[tex]10 X + 15 Y = 8000\\3X + 2Y = 2000[/tex]

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

Substituting value of X in equation 2 we get

[tex]0.3 * 560 + 0.2 Y = 200\\0.2 Y = 200 - 168\\Y = 160[/tex]

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