If John was five years older he would be exactly one-third the age of James. If John was three years younger he would be exactly one-sixth the age of James. How old is James?
Just need help with the equation, thanks.
READ
That was the CHECK
James is 48
Jo + 5 = Ja/3
Jo - 3 = Ja/6
-------------- subtract
0 + 8 = Ja(1/3 - 1/6)
Ja (2/6-1/6) = 8
Ja = 6*8 = 48
===========================
check
Ja = 48
Jo = 3 + Ja/6 = 3 + 8 = 11
then
11+5 = ??? 48/3
16 = 16 sure enough
Just checked if the answer was correct, and unfortunately, it is not.
I understand how you got 16, but I don't understand what is wrong with that equation.
To find the age of James, we can set up two equations based on the given information.
Let's assume John's current age as J and James's current age as M.
According to the first condition, "If John was five years older, he would be exactly one-third the age of James," we can write the equation as:
J + 5 = (1/3)M
According to the second condition, "If John was three years younger, he would be exactly one-sixth the age of James," we can write the equation as:
J - 3 = (1/6)M
Now we have a system of equations:
J + 5 = (1/3)M
J - 3 = (1/6)M
To solve this system, we can use the method of substitution.
First, let's solve the second equation for J:
J = (1/6)M + 3
Now substitute this value of J into the first equation:
(1/6)M + 3 + 5 = (1/3)M
Simplifying the equation:
(1/6)M + 8 = (1/3)M
To eliminate the fractions, we can multiply both sides of the equation by 6:
M + 48 = 2M
Subtracting M from both sides:
48 = M
Therefore, James is 48 years old.