# algebra word problem

• Mar 13th 2009, 10:22 PM
GriceldaM
algebra word problem

A pharmacist has two vitamin-supplement powders. The first powder is 20% vitamin B1 and 10% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each of the two powders should the pharmacist use to make a mixture that contains 130 mg of vitamin B1 and 80 mg of vitamin B2?

any ideas on how to do this?
• Mar 13th 2009, 10:31 PM
u2_wa
Quote:

Originally Posted by GriceldaM

A pharmacist has two vitamin-supplement powders. The first powder is 20% vitamin B1 and 10% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each of the two powders should the pharmacist use to make a mixture that contains 130 mg of vitamin B1 and 80 mg of vitamin B2?

any ideas on how to do this?

Hello GriceldaM
Let x & y be the quantity of first and second powder respectively.
First powder =0.2x (vit B1), 0.1x (vit B2)
second powder =0.15y (vit B1), 0.2y (vit B2)
Vit B1: $\displaystyle 0.2x+0.15y=130$
Vit B2: $\displaystyle 0.1x+0.2y=80$
Solve to get the values of x & y.
• Mar 13th 2009, 10:34 PM
Quote:

Originally Posted by GriceldaM

A pharmacist has two vitamin-supplement powders. The first powder is 20% vitamin B1 and 10% vitamin B2. The second is 15% vitamin B1 and 20% vitamin B2. How many milligrams of each of the two powders should the pharmacist use to make a mixture that contains 130 mg of vitamin B1 and 80 mg of vitamin B2?

any ideas on how to do this?

Lets say he took x milligrams of 1st and y mg of 2nd

-------------------------------------
So composition of 1st powder has

Amount of B1 $\displaystyle = \frac{20 \times x}{100} = \frac{x}{5}$

Amount of B2 $\displaystyle = \frac{10 \times x}{100} =\frac{x}{10}$

---------------------------------
Composition of 2nd powder has

Amount of B1 $\displaystyle = \frac{15\times y}{100} = \frac{3y}{20}$

Amount of B2 $\displaystyle = \frac{20\times y}{100} = \frac{y}{5}$

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

Total composition of B1 and B2 are equated to the given amount of each

$\displaystyle \frac{x}{5} + \frac{3y}{20} = 130$

$\displaystyle \frac{x}{10} + \frac{y}{5} = 80$

Solve these two equations to get x and y