How long has each been teaching?

Question

Three teachers were discussing how long they have been teaching.

-Adrian and Betty have been teaching for a total of 36 years.

-Charlie and Betty have been teaching for a total of 22 years.

-Charlie and Adrian have been teaching for a total of 28 years.

How long has each been teaching?

 

Answer 1

Bailey,

 

Assume Mr. Adrian has been teaching for A years, Ms. Betty for B years and Mr. Charlie for C years

 

A + B = 36

B + C = 22

A + C = 28

 

You have 3 equations in 3 unknowns which can be solved in multiple ways.

 

Adding all 3  equations

2A + 2B + 2C = 86

A + B + C = 43

This is your new eq.

Subtract first eq. from the new eq, C = 7

Subtract second eq from the new eq , A = 21

Subtract third eq. from the new eq:  B = 15

 

This gives you the number of years each has taught.