SOLUTION: Jesse asks his math teacher her age and her husband's age. Jesse's teacher responds that it is not an appropriate question, but that she would use the opportunity to challenge Jess

Algebra ->  Linear-equations -> SOLUTION: Jesse asks his math teacher her age and her husband's age. Jesse's teacher responds that it is not an appropriate question, but that she would use the opportunity to challenge Jess      Log On


   

Question 1106027: Jesse asks his math teacher her age and her husband's age. Jesse's teacher responds that it is not an appropriate question, but that she would use the opportunity to challenge Jesse with a riddle. She says, "One third of my age is ten less than one half of my husband's age. The sum of our ages is 105." How old is Jesse's math teacher?
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
So the problem is reduced to the solution of this system of 2 equations 

%281%2F3%29%2AT = %281%2F2%29%2AH-10     (1)   (T = the teacher's age;  H = the husband's age)

T + H = 105.         (2)


First step is to multiply eq(1) by 6 (both sides) to simplify the system:

2T = 3H - 60         (1')
T  + H = 105.        (2')


Next step is to express  H = 105 - T  from (2') and then to substitute it into eq(1') to get

2T = 3*(105-T) - 60,

2T = 315 - 3T - 60,

2T + 3T = 315 - 60  ====>  5T = 255.


And now YOU make the last step.


I used the Substitution method to solve the system for this problem.