Question

How am I supposed to know why the variable(x in this case) goes on the top or bottom of the fraction? Like from this question. I am confused.

Because of slumping sales, a small company had to lay off some of its employees. The ratio of total employees to employees laid off is 5 to 1. Find the total number of employees if 22 employees were laid off? How would I know?

Answer 1

see explanation

Explanation:

When constructing the ratio to solve, let x be the quantity to be found.

In this case the total number of employees

The 1 part of the ratio represents employees laid off, that is 22

The 5 part of the ratio represents total employees

The x and 5 go together, either on the numerator or denominator

`(5)/(1)` =
`(x)/(22)`

5 and x both on numerator

OR

`(1)/(5)` =
`(22)/(x)`

5 and x both on denominator

Both will lead to the same answer

`(5)/(1)` =
`(x)/(22)` ( cross- multiply )

x = 5 × 22 = 110 ← total number of employees

`(1)/(5)` =
`(22)/(x)` ( cross- multiply )

x = 5 × 22 = 110 ← total number of employees