Hi Liane,
Let's assign some variables first.
Let R=Ron's age
N = Nikki's age
J = Julie's age
From the problem we are told that Nikki is twice as old as Julie. So. N = 2J.
We also know that Ron is 5 years older than Nikki. R = N + 5
Finally we know that R+N+J = 20
So the equations we have are:
1) N = 2 J (Note that this also means that J = N÷2)
2) R = N + 5
3) R + N + J =20
So we can substitute the formulas for J and R that we have in equations 1) and 2) into equation 3). This gives us:
(N+5) + N + (N÷2) = 20
We can combine terms which yields
2N + N/2 + 5 = 20
or, 5N/2 + 5 = 20
From here we can solve for N.
5N/2 = 15
5N = 30
N = 6
So Nikki is 6 years old.
Knowing Nikki's age, we can determine Julie's age from equation 1) J = N/2 = 6/2 = 3. Julie is 3 years old.
Ron's age can be determined from equation 2) R = N + 5 = 6 + 5 = 11. Ron is 11 years old.
And just to double check, let's put all three ages in equation 3).
R + N + J = 20
11 + 6 + 3 = 20.
Hope this helps.
