Question 77030
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)