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1. John’s age is three times that of his sister. When you add John’s age to his sister's age, you get 36. How old are John and his sister?
(a) Write an equation that represents the situation. (1 point)
(b) Solve the equation from Part (a). Show your work. (3 points)
Answer:
Part A: Write an equation.
If the present age is y, then n times the present age = ny.
If the present age is x, then age n years later/hence = x + n.
If the present age is x, then age n years ago = x – n.
The ages in a ratio a: b will be ax and bx.
A(S) + 12 = 3 * A(S), subtracting A(S) from both sides one gets 12 = 2 * A(S). Now dividing both sides by 2 we get A(S) = 12/2 = 6 . Therefore, the age of the sister is 6 years when her brother John is three times as old, that is 18 years.
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