Advanced direct proportion

Percentage increase/decrease = (actual increase/decrease divided by original value) x 100

We sometimes need to find an equation for two quantities that are in proportion.

If a and b are in direct proportion then we can write this as a ∝ b, ∝ is the symbol for proportionality but can be replaced with "= K"

It costs 72p for 12 pencils, work out an equation connecting cost and number of pencils, then find out how much 30 pencils will cost.
Let a be the cost in pence and b the number of pencils, a ∝ b
a = k x b so 72 = k x 12
k = 72 ÷ 12 so k = 6
We can find the equation is a = 6b.
Now, we can calculate the price for 30 by substituting b with 30.
a = 6 x 30 so a = 180p
If a and b are in indirect proportion then a ∝ 1/b.

	Created by megan johnson almost 8 years ago

a set of notes on direct proportion