Quadratic Equation Solution12





In this page quadratic equation solution12 we are going to see solution of the word problems of the topic quadratic equation.

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

quadratic equation solution12 quadratic equation solution12