A parent has two children whose age difference is 5 years. Twice the sum of the ages of the two children is equal to the age of the parent.
(a) Taking x to be the age of the elder child, write an expression for:
(i) the age of the younger child;
(ii) the age of the parent.
(b) In twenty years time, the product of the children's ages will be 15 times the age of their parent.
(i) Form an equation in x and hence determine the present possible ages of the elder child.
(ii) Find the present possible ages of the parent.
(iii) Determine the possible ages of the younger child in 20 years time.
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