If we say that two quantities are in direct proportion, we mean that there is a fixed ratio between them. For instance, if for every $2 that Ann receives Bob will receive $3, then Ann and Bob’s income is in direct proportion.

Solving problems of direct proportion are effectively the same as solving ratio problems where instead of knowing the total quantity, we only know the quantity of a part.

For instance, suppose Bob had $150, then how much money does Ann have.

Similarly to the previous problems, we divide Bob’s $150, but not by the total, only by Bob’s “ratio number”, i.e. $150 ÷ 3. This gives us the value of 1 part, i.e. $50. So Ann receives 2 x $50 = $100.

Example

Exercise

Let’s complete the following exercise:

Answers