SOLUTION: Next year, Lyle will be twice as old as Sean will be. Four years ago, he was three times as old as Sean was. How old is each?

Question 77030This question is from textbook Algebra Structure and Method
: Next year, Lyle will be twice as old as Sean will be. Four years ago, he was three times as old as Sean was. How old is each? This question is from textbook Algebra Structure and Method

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Next year, Lyle will be twice as old as Sean will be. Four years ago, he was three times as old as Sean was. How old is each?
:
Let L = Lyle's age now; Let S = Sean's age now;
:
"Next year, Lyle will be twice as old as Sean will be."
L + 1 = 2(S + 1)
L + 1 = 2S + 2
L = 2s + 2 - 1
L = 2s + 1
:
"Four years ago, he was three times as old as Sean was."
L - 4 = 3(S - 4)
L - 4 = 3S - 12
L = 3S - 12 + 4
L = 3S - 8
:
Substitute (2s+1) for L and find S
2S + 1 = 3s - 8
1 + 8 = 3s - 2s
S = 9 yrs is Sean's age now
:
Find L using the 1st equation
L = 2(9) + 1
L = 19 yrs is Lyle's age now
:
Check solution using the 4 yrs ago equation:
19 - 4 = 3(9 - 4)
15 = 3(5)
:
Check using next year
19 + 1 = 2(9 + 1)
20 = 2(10)

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