Anthony T. answered • 02/06/21
Patient Science Tutor
This was tricky! Let Yn = Juan's age now, and Jn be Jose's age now. We have to figure how to represent Jose's age when Juan was as old as Jose is now. Juan is Yn - Jn years older than Jose, so when Juan was Jose's age, Jose was Jn - (Yn -- Jn) = 2Jn - Yn. So, the first expression in the problem can be written as
Yn = 3(2Jn - Yn). The second expression asks how old will Juan be when Jose is 2Yn. Jose's age in the future is 2Yn. Juan's age in the future will be Jose's age in the future plus the difference between their ages which is Yn - Jn, the sum of which must be 78. Algebraically, this is 2Yn + 2Yn + Yn - Jn = 78. This simplifies to 5Yn - Jn = 78 or Jn = 5Yn - 78. This Jn can be substituted in the equation given previously, Yn = 3(2Jn - Yn) and solved for Yn. Yn turns out to equal 18 and then solving for Jn = 12.
Do the algebra yourself to see if you agree with me.
Anthony T.
The results I obtained satisfy the equation Yn = 3(2Jn - Yn). If Jn is 12 then 2Jn =24. If Yn = 18 then 2Jn -Yn = 6, then 3x6 = 18 which is Juan's age now.02/07/21
Katsuo M.
I agree with your second expression but I think your first expression has a typo. Shouldn't it be Jn = 3(2Jn - Yn) since we're talking about Juan's age from before = Jose's age now?02/06/21