Answer:
The three ages are { 15, 20, 31 }
Step-by-step explanation:
Let the ages of these three people be x, y and z, in ascending order.
Then:
x + y + z
------------ = mean age = 22. This leads to x + y + z = 3(22) = 66.
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If the median age is 20, then y = 20, since y (20) is the middle value.
If the range of their ages is 16, then z - x = 16.
Rewrite x + y + z = 66 as x + 20 + z = 66, or x + z = 46.
Solve the system
-x + z = 16
x + z = 46
for x and z. To do this, combine these two equations, obtaining:
2z = 62, so that z = 31.
Use z - x = 16 with z = 31 to find the value of x:
-x + 31 = 16, or -x = -15. Then x = 15.
The three ages are { 15, 20, 31 }.
Check: is the mean (average) of these three ages equal to 22?
Does:
15 + 20 + 31
------------------- = 22? Does (35 + 31)/3 = 22? YES
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