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Question: Alice is four years older than Bob who is thrice as old as Cija. If the total of the ages of Alice, Bob and Cija be 39, the how old is Bob?

Solution:
Let age of Cija = x

Age of Bob = Thrice as old as Cija = 3x

Age of Alice = Four years older than Bob = 3x + 4

The problem states:

x + 3x + (3x + 4) = 39

=> 4x + 3x + 4 = 39

=> 7x = 39 - 4 = 35

=> x = 5, age of Cija

Hence, Age of Bob = 3 x 5 = 15.

=> Bob is of 15 years.

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## Solved Examples

Question 1: Five times a number plus four times its reciprocal is 21. Find the number.
Solution:
Let number = x

The problem states:

5 times a number plus 4 times its reciprocal is 21

=> 5x + $\frac{4}{x}$ = 21

=> $\frac{5x^2 + 4}{x}$ = 21

=> 5x2 + 4 = 21x

=> 5x2 - 21x + 4 = 0

=> 5x2 - 20x - x + 4 = 0

=> 5x(x - 4) - (x - 4) = 0

=> (5x - 1)(x - 4) = 0

either 5x - 1 = 0   or   x - 4 = 0

=> x = $\frac{1}{5}$  or  x = 4

Question 2: Find three consecutive even integers such that the largest is twice the smallest.

Solution:
Let first integer = x (Smallest)

Second consecutive even integer = x + 2

Third consecutive even integer = x + 4 (Largest)

Since largest is twice the smallest integer

=> x + 4 = 2x

=> x = 4

Hence,
First integer = 4,

Second integer = x + 2 = 4 + 2 = 6,

Third integer = x + 4 = 4 + 4 = 8.