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Proportion Equations

Proportion Equations

Where two terms are in direct proportion to one another, it is written as

yx

where y and x are general terms; for example, x could be x3. It is said as y is in proportion to x. But if they are in direct proportion, then one is a multiple of another. This direct proportion can be re-written as:

y=kx

where k is a number called the constant of proportionality.

Given two values for x,y and k, the third value can be derived.

Example 1

y is proportional to x. When y=30,x=10. What is the constant of proportionality?

yx

Re-write as y=kx

Substituting for y and x

30=k×10 and solve for k=3

Answer: 3

Example 2

y is proportional to x2. When y=3,x=6. What is the value of x when y=6? Give your answer correct to two decimal places.

y(x2)

Therefore y=kx2

Substituting: 3=k(62) and solve for k=336=112

When y=6, and using k=112,

6=112x2

x=8.485=8.49 (2dp)

Answer: 8.49