SOLUTION: Thelma is a fifty one year old mother of three children. The difference in ages between the oldest and the middle child is two years. The difference in ages between the youngest an

Question 772766: Thelma is a fifty one year old mother of three children. The difference in ages between the oldest and the middle child is two years. The difference in ages between the youngest and the oldest child is four years. If Thelma's age is equal to the sum of the ages of all three of her children, how old are each of her children, how old are each of her children?

Answer by pakhi(24) (Show Source): You can put this solution on YOUR website!
Let the age of the eldest child be E yrs.
Let the age of the middle child be M yrs.
Let the age of the youngest child be Y yrs.
Therefore according to the problem
Condition 1 E - M = 2 or M = E - 2 -------------(1)
Condition 2 E - Y = 4 or Y = E - 4 -------------(2)
Condition 3 E + M + Y = 51 ---------------------(3)
Substituting the values of M and Y from equations 1 and 2 in 3 we get
E + (E - 2) + (E - 4) = 51
or E + E - 2 + E - 4 = 51
or 3E - 6 = 51
or 3E = 51 + 6 = 57
or E = 57/3 = 19
So M = E - 2 = 19 - 2 = 17
Also Y = E - 4 = 19 - 4 =15
Hence the ages of the three children are respectively 19yrs, 17yrs, 15yrs.
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