Question 980579

    -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?
<pre>Let number of years Adrian, Betty, and Charlie have been teaching be A, B, and C, respectively
We then get: 
A + B = 36______B = 36 - A -------- eq (i)
C + B = 22 -------- eq (ii)
C + A = 28 -------- eq (iii)

C + 36 - A = 22 ----- Substituting 36 - A for B in eq (ii) 
C - A = 22 - 36 
C - A = - 14 -------- eq (iv)
2C = 14 ------------- Adding eqs (iii) & (iv)
C, or amount of time Charlie has been teaching = {{{14/2}}}, or {{{highlight_green(7)}}} years

7 + B = 22 ---------- Substituting 7 for C in eq (ii)
B = 22 - 7
B, or amount of time Betty has been teaching = {{{highlight_green(15)}}} years

7 + A = 28 ---------- Substituting 7 for C in eq (iii)
A = 28 - 7
A, or amount of time Adrian has been teaching = {{{highlight_green(21)}}} years