Vernice did not want to tell her age, so when she was asked, her mother answered forher. Her mother said, "I am double her age plus 10.In ten years' time she will be half my age. How old is Vernice?
Accepted Solution
A:
Answer:The age of vernice can be any multiple of 5.
Explanation:Given:Vernice did not want to tell her age, so when she was asked, her mother answered for her. Her mother said, "I am double her age plus 10. In ten years' time she will be half my age. To find:how old is Vernice?
Solution:Now, mother's age = double of vernice age + 10 years present age of mother = 2 x vernice present age + 10................. (1)
Now, after 10 years (present age of mother + 10) = 2 x ( present age of vernice + 10 years).....................(2)
Assumption 1:Now, let us assume that, age of mother be 30 ,Then, from 1st equation 30 = 2 x vernice age + 10 2 x vernice age = 30-10
2 x vernice age = 20[tex]vernice age =\frac{20}{2}[/tex] vernice age = 10
Now, put above assumptions in (2) 30 + 10 = 2 (10 + 10 ) 40 = 2 x 20 40 = 40 So, our assumption is true.
Assumption 2:Now, let us assume that, age of mother be 40 , Then, from 1st equation 40 = 2 x vernice age + 10 2 x vernice age = 40-10 2 x vernice age = 30 [tex]\text{{vernice age}} =\frac{30}{2}[/tex] vernice age = 15
Now, put above assumptions in (2) 40 + 10 = 2 (15 + 10 ) 50 = 2 x 25 50 = 50 So, our assumption is true again.
So, for any multiple of 5 as vernice age in above equations, situation becomes possible.
Hence, the age of vernice can be any multiple of 5.