SOLUTION: Eighteen years ago, Benjamin was eight more than one-third as old as Jessica. Today, Jessica is twenty less than two times the age of Benjamin. How old is Jessica?

Question 723796: Eighteen years ago, Benjamin was eight more than one-third as old as Jessica. Today, Jessica is twenty less than two times the age of Benjamin. How old is Jessica?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let b = B's present age
Let j = J's present age
;
Write an equation for each statement:
:
Eighteen years ago, Benjamin was eight more than one-third as old as Jessica.
b - 18 = (j - 18) + 8
multiply both sides by 3
3(b-18) = j - 18 + 3(8)
3b - 54 = j - 18 + 24
3b = j - 18 + 24 + 54
3b = j + 60
:
Today, Jessica is twenty less than two times the age of Benjamin.
j = 2b - 20
:
replace j with (2b-20) in the 1st simplified equation
3b = (2b-20) + 60
3b - 2b = 60 - 20
b = 40 yrs old is B
:
find j
j = 2(40) - 20
j = 60 yrs is Jessica's age
:
:
:
Check this in the 1st original equation
40 - 18 = (60 - 18) + 8
22 = (42) + 8
22 = 14 + 8

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