*In inverse variation, it's exactly the opposite: as one number increases, the other decreases. An example would be the relationship between time spent goofing off in class and your grade on the midterm.*

*In inverse variation, it's exactly the opposite: as one number increases, the other decreases. An example would be the relationship between time spent goofing off in class and your grade on the midterm.*The more you goof off, the lower your score on the test.This might seem really complicated and confusing, but just remember the two formulas: y = kx for direct variation, and y = k/x for inverse variation.

If we wanted to give this one an equation, we would say: y = k/x, where x and y are the two quantities, and k is still the constant of proportionality, telling how much one varies when the other changes.

You can see that in this equation, you divide a constant number by x to get the value of y.

Again, not a problem: just plug in 'b 3' for the value of x on the bottom of the fraction. In this lesson, you learned how to tackle direct and inverse variation problems by using the equations for each.

That's most of the work done already: now we have an equation relating a and b. For direct variation, use the equation y = kx, where k is the constant of proportionality.

The next step is to use that value to find out how many millions of bacteria there are at 38 degrees Celsius. This time, we'll plug in x and k, since we're looking for y. Do the multiplication, and we learn that y, or the value of the population in millions is 7.6. If k represents the constant of proportionality, then in terms of b and k, what is the value of a?

So the answer to this question would be 7.6 million bacteria. This one is a tough nut to crack because the problem gives you a value for a squared, but asks you about the value of a.

In this problem, we're trying to isolate a, so it makes more sense to put it all by itself on one side of the equation; this will make the math easier later on.

Next, we have 'the sum of 3 and b, or in math terms, b 3 instead of plain old b.

Now let's plug in what we have from the problem: The problem gives us two values: temperature and number of bacteria.

We'll plug in the temperature for x and the number of bacteria for y. Now all we have to do is divide to find the value of k for this particular problem: it turns out to be 0.2. The square of a varies inversely with the sum of three and b.

## Comments Inverse Variation Problem Solving

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