The mean age of three people is 22 and their median age is 20. The range of their age is 16. How old is each person

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.      3If 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 = 16x + z = 46for 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           3