Question

In a certain company, the ratio of the number of managers to the number of production-line workers is 5 to 72. if 8 additional production line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. how many managers does the company have?

Answer 1

Let the number of the production line workers be x.

The ratio of managers to workers is 5 : 72hence the number of managers will be :

5/72x

When 8 more workers are added the total number of workers become x + 8

The new ratio should be:

5/72x : x + 8

This is equal to 5 : 74

We equate the two :

(5/72x) / (x + 8) = 5/74

Solving for x we have :

(5/72 × 74) = 5 × (x + 8)

370/72x = 5x + 40

370x = 5x × 72 + 40 × 72

370x = 360x + 2880

370x - 360x = 2880

10x = 2880

x = 288

The number of managers is :

5/72 × 288 = 20