SOLUTION: the four oldest people in Golden City have lived 384 years. the difference in ages for the youngest and the next oldest is 14. the next youngest is 3 years older than the youngest.

Question 149563: the four oldest people in Golden City have lived 384 years. the difference in ages for the youngest and the next oldest is 14. the next youngest is 3 years older than the youngest. the oldest is 20 years older than the average of the next oldest and youngest. How old is each?
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the four oldest people in Golden City have lived 384 years. the difference in ages for the youngest and the next oldest is 14. the next youngest is 3 years older than the youngest. the oldest is 20 years older than the average of the next oldest and youngest. How old is each?
:
Let the 4 people be w,x,y,& z (youngest to oldest)
:
Write an equation for each statement
:
"the four oldest people in Golden City have lived 384 years."
w + x + y + z = 384
:
"the difference in ages for the youngest and the next oldest is 14."
y - w = 14
y = w + 14
:
"the next youngest is 3 years older than the youngest.
x = w + 3
:
the oldest is 20 years older than the average of the next oldest and youngest.
z = + 20
multiply equation by 2 to get rid of the denominator
2z = w + y + 2(20)
2z = w + y + 40
Replace y with (w+14)
2z = w + (w+14) + 40
2z = 2w + 54
Divide equation by 2:
z = w + 27
:
How old is each?
:
Replace x, y, and z in the total equation with the above equations:
w + (w+3) + (w+14) + (w+27) = 384
:
4w + 44 = 384
:
4w = 384 - 44
:
4w = 340
w =
w = 85 yrs is the youngest oldie
then
x = 85 +3
x = 88 yrs is the next oldie
and
y = 85 + 14
y = 99 yrs
and
z = 85 + 27
z = 112 yrs is real old guy
;
:
Check solution by finding the total
85 + 88 + 99 + 112 = 84
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