anyone outh there who could possibly help me and show me how to do this math problem?

Question

blues varied directly as greens and inversely as whites squared, and 4 blues and 2 whites went with 3 greens. how many greens were required for 2 blues and 4 whites? work the problem once using the variation method and again using the equal ratio method.

Answer 1

I'm honestly not sure what the methods your teacher wants you to use are (and the best way to find out would be to consult your textbook or your teacher, rather than Y!A). I can tell you what the terms mean: blues vary directly as greens means that the number of blues is equal to some constant times the number of greens. Blues vary inversely was whites squared means that it is equal to some constant divided by the square of the number of whites. So in this case, we have the equation:

b=kg/w², where k is the unknown constant of proportionality.

Now one way to solve this problem (and the way I'd do it, although I don't know whether it corresponds to either of the methods your teacher wants you to use) is to use the initial conditions to solve for k, and then use the knowledge of k and the final conditions to solve for g. For the first part:

4=k*3/2²

Multiplying by 4/3:

k=4*4/3=16/3

Now using the second part:

2=16/3 * g/4²

The 16 cancels the 4², so:

2=g/3

Multiplying by 3 yields:

g=6.

And we are done.