SOLUTION: Jon is 3 x Jacs age. Jill is 1/3 of Jacs age. Jon is 16 years older than Jill How old is Jac?

Question 1158252: Jon is 3 x Jacs age.
Jill is 1/3 of Jacs age.
Jon is 16 years older than Jill
How old is Jac?
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
---------------------------
Jon is 3 x Jacs age.
Jill is 1/3 of Jacs age.
Jon is 16 years older than Jill
How old is Jac?
-----------------------------

What is the "x" ? Multiplication?

j, Jacs age
Jon,
Jill,
Joh,

TWO of the expressions are Jon's age, in terms of Jac's age. Form the equation and solve.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let Jon’s age be , Jac’s age , and Jill’s age
if Jon is times Jac’s age, we have
.....eq.1
Jill is of Jac’s age, we have
.....eq.2
if Jon is years older than Jill, we have
....eq.3.......substitute from eq.2

.......eq.3a
from eq.1 and eq.3a we have
........solve for
....both sides multiply by

=> Jac is years old

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

It can be solved in much easier manner.

Let x be the age of Jill, who is the youngest. The the Jac's age is 3x, while the Jon age is 3*(3x) = 9x. Jon is 16 yaers older than Jill 9x - x = 16. It implies 8x = 16 x = 16/8 = 2. So, Jill is 2 years old. Hence, Jac is 3x = 3*2 = 6 years old. ANSWER

Solved.

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