The sum of the ages of Sindu and Bindu is 30 years. The product of their ages is 221. Find their ages.(answer=17 & 13 years explain)
Answers
Solution :-
Let the age of Sindu and Bindu be 'x' years and 'y' years
Sum of ages of Sindu and Bindu = 30 years
⇒ x + y = 30
⇒ y = 30 - x
Product of their ages = 221
⇒ xy = 221
⇒ x(30 - x) = 221
⇒ 30x - x² = 221
⇒ 0 = x² - 30x + 221
⇒ x² - 30x + 221 = 0
Splitting the middle term
⇒ x² - 17x - 13x + 221 = 0
⇒ x(x - 17) - 13(x - 17) = 0
⇒ (x - 13)(x - 17) = 0
⇒ x - 13 = 0 or x - 17 = 0
⇒ x = 13 or x = 17
When Sindu's age x = 13 years
Bindu's age y = 30 - x = 30 - 13 = 17 years
When Sindu's age x = 17 years
Bindu's age y = 30 - x = 30 - 17 = 13 years
Therefore their ages are 13 years and 17 years.
Answer:
Step-by-step explanation:
Given :-
Sum of Ages of Sindu and Bindu = 30 years.
Product of Ages of Sindu and Bindu = 221 years.
To Find :-
Their Ages.
Solution :-
Let the age of Sindu be x years
And Bindu be y years.
According to the Question,
Sum of Ages = 30 years
⇒ x + y = 30
⇒ y = 30 - x
Product of Ages = 221 years
⇒ xy = 221
Putting y's value, we get
⇒ x(30 - x) = 221
⇒ 30x - x² = 221
⇒ 0 = x² - 30x + 221
⇒ x² - 30x + 221 = 0
⇒ x² - 17x - 13x + 221 = 0 [ By Splitting middle term ]
⇒ x(x - 17) - 13(x - 17) = 0
⇒ (x - 13)(x - 17) = 0
⇒ x - 13 = 0 or x - 17 = 0
⇒ x = 13 or x = 17
When Sindu's Age x = 13 years
Bindu's Age = 17 years
When Sindu's Age x = 17 years
Bindu's Age = 13 years
Hence, their ages are 13 years and 17 years.