#Unit4

Compound proportion is a mathematical concept that deals with a change in one quantity that depends on the changes in two or more other quantities, which can be either directly or inversely proportional. It is used to solve problems involving multiple variables, such as how many men are needed to finish a job in a certain number of days, or how many items can be produced with a different number of machines and days. To solve, you can set up an equation that represents the relationships between the variables. 

How to solve compound proportion problems

Identify the variables: Determine the quantities involved and the unknown value you need to find. For example, in a problem about men, days, and hours, the variables are men, days, and hours.

Determine the relationship: For each variable, figure out if it is directly or inversely proportional to the unknown variable.

Direct proportion: If the unknown variable increases, this variable also increases.

Inverse proportion: If the unknown variable increases, this variable decreases.

Set up the equation: Create a proportion using the given information and your variable relationships.

Example: If the unknown (



) is in the third column and you have the relationship:

Quantity 1 and Quantity 2 are directly related.

Quantity 2 and Quantity 3 (the unknown) are inversely related.

The equation would be set up as: 



.

Solve for the unknown: Cross-multiply and solve for the unknown variable, 



. 

Example problem

Problem: If 195 men working 10 hours a day can finish a job in 20 days, how many men are required to finish the job in 15 days if they work 13 hours a day?

Variables: Men, hours, and days.

Unknown: Number of men (



).

Relationships:

Men and Days: Inverse (more men, fewer days)

Men and Hours: Inverse (more hours, fewer men)

Setup: 



Solution: 



 men