The four oldest people in Golden City have lived a total of 384 years put together. The difference in ages for the youngest and the second oldest is 14. The second youngest is 3 years older than the youngest. The oldest is 20 years older than the average of the second oldest and youngest find their ages and enter them from youngest to oldest.
In order youngest to oldest, we have a,b,c,d where
a+b+c+d = 384
c-a = 14
b = a+3
d = 20+(c+a)/2
85,88,99,112
To solve this problem, we can write a system of equations based on the given information:
Let's say the ages of the four oldest people in Golden City are represented by variables: Y (youngest), SY (second youngest), SO (second oldest), and O (oldest).
1. The four oldest people have lived a total of 384 years put together:
Y + SY + SO + O = 384
2. The difference in ages for the youngest and the second oldest is 14:
O - Y = 14
3. The second youngest is 3 years older than the youngest:
SY = Y + 3
4. The oldest is 20 years older than the average of the second oldest and youngest:
O = (SO + Y) / 2 + 20
We have four equations and four unknowns, so we can solve this system of equations to find the values of Y, SY, SO, and O.
Let's solve these equations step by step:
First, simplify equation 4:
2O = SO + Y + 40
2O - SO = Y + 40
Now, substitute the simplified equation 2 (O - Y = 14) into the simplified equation 3 (SY = Y + 3):
O - 14 = Y + 3
O = Y + 17
Substitute the value of O (Y + 17) into the simplified equation 4:
2(Y + 17) - SO = Y + 40
2Y + 34 - SO = Y + 40
Y - SO = 6 (equation 5)
Now, let's rewrite equation 1 using the value of O (Y + 17):
Y + SY + SO + (Y + 17) = 384
2Y + SY + SO = 367 (equation 6)
We now have two equations remaining: Equation 5 (Y - SO = 6) and Equation 6 (2Y + SY + SO = 367).
By solving these two equations simultaneously, we can find the values of Y, SY, SO, and O.
However, in order to find the exact numerical values, we need additional information or constraints from the question.