Emerson's family consists of five members and the sum of the ages of his family members is 138. His mother's age which is a two digit number is exactly the reverse of his father's age. His younger sister's age is equal to the sum of the digits of his mother's age. His elder brother is twice as old as his sister. Emerson is 3 years elder to his sister. The difference between the age of his brother and his sister is equal to the difference between the ages of his parents. What are the ages of his father and mother?
Answers
5×3=15
138+15=153
I hope this will help you
If helpful then please select my answer as brainliest answer
And also follow me ❤️❤️❤️❤️❤️❤️❤️❤️
Answer:
Let the age of Father = 10x+y
According to the question,
Age of mother = 10y+x,
Age of sister = y+x
Age of brother = 2(y+x)
Age of Emerson = y+x+3,
∵ The difference between the age of his brother and his sister is equal to the difference between the ages of his parents.
i.e. 2(x+y)-(x+y) = 10x+y - (10y+x)
x+y =9x - 9y
10y = 8x ----(1),
Now, the sum of ages of all family members = 10x+y+10y+x+y+x +2(y+x )+y+x+3 = 15x + 15y + 3
Again according to the question,
15x + 15y + 3 = 138
15x + 15y = 135
x + y = 9
8x + 8y = 72 ----(2),
From equations (1) and (2),
10y + 8y = 72
18y = 72
⇒ y = 4,
Again from equation (1),
40 = 8x
⇒ x = 5
Hence, the age of father = 10x + y = 50 + 4 = 54 years,
The age of mother = 10y + x = 45 years