Setting Up Correct Equations...4

mathdad

mathdad

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Apr 24, 2015
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A doctor’s prescription calls for the creation of pills that contain 12 units of vitamin B12 and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: One contains 20 percent vitamin B12 and 30 percent vitamin E, the other 40 percent vitamin B12 and 20 percent vitamin E. How many units of each powder should be mixed in each pill?

Set Up:

Let x = vitamin B12

Let y = vitamin E

0.20x + 0.30y = 12
0.40x + 0.20y = 12
 
Why do I bother to give a systematic way of thinking?.

Step 1: Identification and Labeling.

[MATH]x = \text {units of 20B/30E mix, and} \\ y = \text {units of 40B/20E mix.}[/MATH]Two unknowns. What do you know?

Step 2: translating.

The final result must have 12 units of B, and the B comes from two powders containing respectively 20% and 40%. So, translating into math

[MATH]0.2x + 0.4y = 12.[/MATH]
The final result must also have 12 units of E, and the E comes from two powders containing respectively 30% and 20%. So, translating into math

[MATH]0.3x + 0.2y = 12.[/MATH]
Now it is all mechanical.
 
This labeling isn't quite correct is it.

What x really is is the amount of the first powder with the 0.2/0.3 mix
and y is the amount of the powder with the 0.4/0.2 mix.

And thus the equations should be

0.2x + 0.4y = 12 (the B12)
0.3x + 0.2y = 12 (the Vitamin E)
 
JeffM said:
Why do I bother to give a systematic way of thinking?.

Step 1: Identification and Labeling.

[MATH]x = \text {units of 20B/30E mix, and} \\ y = \text {units of 40B/20E mix.}[/MATH]Two unknowns. What do you know?

Step 2: translating.

The final result must have 12 units of B, and the B comes from two powders containing respectively 20% and 40%. So, translating into math

[MATH]0.2x + 0.4y = 12.[/MATH]
The final result must also have 12 units of E, and the E comes from two powders containing respectively 30% and 20%. So, translating into math

[MATH]0.3x + 0.2y = 12.[/MATH]
Now it is all mechanical.
Click to expand...

I assigned 0.20, 0.30 and 0.40 to the wrong variables. I give myself credit for at least setting up two equations, wrongly, but two equations nonetheless.
 
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