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?

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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) About Me  (Show Source):
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Jon is 3 x Jacs age.
Jill is 1/3 of Jacs age.
Jon is 16 years older than Jill
How old is Jac?
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What is the "x" ? Multiplication?

j, Jacs age
Jon, 3j
Jill, %281%2F3%29j
Joh, j%2F3%2B16

TWO of the expressions are Jon's age, in terms of Jac's age. Form the equation and solve.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


let Jon’s age be x, Jac’s age y, and Jill’s age z
if Jon is 3 times Jac’s age, we have
x=3y.....eq.1
Jill is 1%2F3+of Jac’s age, we have
z=%281%2F3%29y.....eq.2
if Jon is 16 years older than Jill, we have
x=z%2B16....eq.3.......substitute z from eq.2

x=%281%2F3%29y%2B16.......eq.3a
from eq.1 and eq.3a we have
3y=%281%2F3%29y%2B16........solve for y
3y-%281%2F3%29y=16....both sides multiply by 3
9y-y=48
8y=48
y=6=> Jac is 6 years old

Answer by ikleyn(52788) About Me  (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.