Question 19

The sum of the age of a man and his son is 35 years and the product of their ages is 150. Find their ages.

Solution:

Here the age of man is compared with his son.

So let us take “x” as a man’s age

And “y” as his son’s age

Sum of the age of a man and his son is 35

x + y =35

y = 35 – x  ------ (1)

Product of their ages is 150.

x y = 150 ---- (2)

Now we are going to apply the value of y that is y = 35 – x in the second equation to make the given equation in one variable

x (35 – x) = 150

35 x – x² = 150

x²  -35 x + 150 = 0

x² - 30 x – 5x  + 150 = 0

x (x – 30) - 5 (x – 30) = 0

(x – 5) (x - 30) = 0

x – 5 = 0                   x – 30 = 0

x = 5                            x = 30

Here x represent the man’s age so it should not be 5.

Now we are going to apply x = 30 in the first equation inorder to get the value of y that is his son’s age

y = 35 – 30

y = 5

Therefore the age of the man is 35 and his son is 5.

Verification:

The sum of the age of a man and his son is 35 years

30 + 5 = 35

35 = 35

the product of their ages is 150

30 ( 5 ) = 150

150 = 150