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Let K = Kayla's age now, Let N = Nathan's age now
Kayla would be one-half as old as Nathan if Kayla were 4 years older.
Kayla 4 yrs older = (K+4)
The statement says:
(K+4) = .5N
or we can say:
K = .5N - 4
Nathan is eight less than three times as old as Kayla.
N = 3K - 8
How old are they?
We can substitute (.5N-4) for K in the above equation and find N
N = 3(.5N-4) - 8
N = 1.5N - 12 - 8
N = 1.5N - 20
N - 1.5N = -20
-.5N = - 20
N = -20/-.5
N = + 40 yrs is Nathan's age now
We know K = .5N - 4
K = .5(40) - 4
K = 20 - 4
K = 16 yrs is Kayla's age now
Check our solutions in the statement:
"Nathan is eight less than three times as old as Kayla."
40 = 3(16) - 8
40 = 48 - 8; confirms our solutions
Did this make sense to you? Any questions?