Question

A quantity a varies inversely as a quantity b, if, when b changes, a changes in the inverse ratio. What happens to the quantity a if the quantity b doubles? a. quantity a triples c. quantity a stays the same b. quantity a doubles d. quantity a halves

Answer 1

d. quantity a halves

Explanation:

a = k/b

k = a × b

If b doubles, a halves

Answer 2

D

Explanation:

When we see these inverse proportion problems, we think of the generic form of : y = k/x, where y varies inversely to x and k is a constant.

In this case, y = a and x = b: a = k/b

Now, since b doubles, we have 2b, so: a = k/2b. Since we are dividing by an extra 2 (there's now a 2 in the denominator), a is actually halved.

Thus, the answer is D.

Hope this helps!