In 3 years, Nell will be twice as old as Ruth is now. Two years ago, the sum of their ages was 20. find how old Nell and Ruth are now
Answers
Answer:
Today Nell is 15 years old
and Ruth is 9 years old....
Step-by-step explanation:
let today's age of Nell's age be 'x'
Ruth's age be 'y'
so let's form equations by given information
so,
in coming 3 years Nell will be twice as old as today's age of Ruth
x + 3 = 2y
x - 2y = -3 ............ (1)
two years ago the sum of their ages was 20 years
thus ,
(x -2) + (y-2) = 20
x +y - 4 = 20
x + y = 24 ....... (2)
by (2) - (1)
x + y = 24
- (x - 2y = -3)
∴ 3y = 27
∴ y = 9
put y = 9 in (1) ,
x -2( 9 ) = -3
x -18 = -3
∴ x = 15
thus answers are satisfied........
hope this answer found to be helpfulll .......
Answer :-
Age of Nell is 15 years and age of Ruth is 9 years.
Explanation :-
Let the age of Nell be 'a' years
Let the age of Ruth be 'b' years
Given
Age Nell after 3 years = twice the age of Ruth
⇒ a + 3 = 2b
⇒ a = 2b - 3 ---eq(1)
Age of Nell 2 years ago = (a - 2) years
Age of Ruth 2 years ago = (b - 2) years
Given
Sum of their ages two years ago = 20
⇒ Age of Nell 2 years ago + Age of Ruth 2 years ago = 20
⇒ (a - 2) + (b - 2) = 20
⇒ a - 2 + b - 2 = 20
⇒ a + b - 4 = 20
⇒ a + b = 20 + 4
⇒ a + b = 24 ---eq(2)
Substitute eq(1) in eq(2)
⇒ (2b - 3) + b = 24
⇒ 2b - 3 + b = 24
⇒ 3b - 3 = 24
⇒ 3b = 24 + 3
⇒ 3b = 27
⇒ b = 27/3
⇒ b = 9
∴ the age of Ruth is 9 years
Substitute b = 9 in eq(1)
⇒ a = 2b - 3
⇒ a = 2(9) - 3
⇒ a = 18 - 3
⇒ a = 15