Creating a table from a system of linear equations

[armolinasf]

Homework Statement

A doctor's prescription calls for a daily intake of liquid containing 40mg of vitamin c and 30mg of vitamin d. There are three liquids that can be used: one contains 20%vitamin c and 30% vitamin d; the second, 40% vitamin c and 20% vitamin d; the third, 30% vitamin c and 50% vitamin d.

Create a table showing the possible combinations that could be used to fill the prescription.

The Attempt at a Solution

I'm not quite sure how to approach this one. I'm thinking of setting it up as a system of linear equations with three variables. I'm having trouble relating the percentages to the amount in grams. Thanks for the help.

 

[CompuChip]

That sounds like a good idea. The three variables you would use (let's call them x, y, z) would then correspond to the amount of liquid you take from each of the three types.
I would choose grams as units for x, y, z; so for example x = 120 corresponds to taking 120 g of liquid one. Then you can easily express the amount of vitamins in terms of x, y and z and draw up your system of equations.