Question

If a = 3b^3/c, what happens to a when b is doubled?

Answer 1

a becomes 8 times larger when b is doubled. Let's take the original expression 3b^3/c and effectively double b by multiplying by 2. Then we will take the new expression and divide by the old expression and see what happens. a = 3b^3/c a' = 3(2b)^3/c a'/a = 3(2b)^3/c / 3b^3/c You can divide by a fraction by swapping the top and bottom and then multiplying. So a'/a= 3(2b)^3/c * c/3b^3 The c terms cancel, giving: a'/a= 3(2b)^3/1 * 1/3b^3 The 3's cancel, giving: a'/a= (2b)^3/1 * 1/b^3 Expand the parenthesis a'/a= 8b^3/1 * 1/b^3 Cancel the b^3 terms a'/a= 8/1 * 1/1 = 8 * 1 = 8 So a' is 8 times larger than a.