A Problem From Project InterMath

Find as many solutions as possible for A, B, and C that satisfy both equations:

ABC = 4 and 3A + 2B - C = 3.

What observations can you make about your results?

## Discussion:

That is a rather vague and open ended question about your results.

Note that the problem does not specify that A, B, and C should be integers. Hence you should explore both possibilities.

For the moment, assume we want to find integer values.

You might want to explore graphing the figures with your own software.

## A strategy Hint

Fix the value of C (or z) and explore the problem for locating the other two values.

Repeat for several values of c.

This strategy could use

Spreadsheets

Graphing

For example, if z = 1, our two-dimensional

graphof xy = 4 and 3x + 2y - 1 = 3 is at the right. The red curve and the blue curve do not intersect. This tells us there is no solution when C = 1.Make additional graphs for C = 2, 3, 4, etc. and C= -1, -2, - 3, etc.

Alternatively, we could make spread sheet exporation for the different values of C

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