if twice the son's age in years is added to the father's age, the sum is 70. but if twice the father's age is added to the son's age , the sum is 95. what is the age of the son ?
Answers
according to the conditions,
2y+x=70 ..............(1)
2x+y=95 ..............(2)
multiplying equation (1) into 2 we get
subtracting equation (2) from equation (3)
4y+2x=140 .........(3)
y+2x= 95
---------------
3y = 45
y=15 ..................(4)
substituting (4) in (2) we get
15 +2x=95
2x=80
x=40.
Therefore the age of the father is 40yrs and that of the son is 15 yrs
The Son age is 15 years
Explanation:
Given:
1. Twice the son's age in years is added to the father's age, the sum is 70
2. Twice the father's age is added to the son's age , the sum is 95.
To find:
The age of son
Solution:
==> Son age = x
==> Twice the son age = 2x
==> Father age = y
==> Twice the father age =2y
==> twice the son age is added to the father age sum is 70
==> twice the son age + the father age = 70
==> Write this in equation
==> 2x+y = 70 ==>1
==> twice the father age is added to the son age sum is 95
==> twice the father age + the son age = 95
==> 2y + x = 95
==> x+2y =95 ==>2
==> using Substitution Method
==> Rewrite the 2nd equation
==> x = 95-2y ==>3
==> Substitute equation 3 in 1
==> 2x+ y =70
==> 2(95-2y)+y =70
==> 190 -4y+y = 70
==> 190-3y = 70
==> 3y = 190-70
==> 3y =120
==> y = 40 years
==> Substitute y value in equation 3
==> x =95-2y
==> x = 95-2(40)
==> x = 95-80
==> x = 15 years
The Son age is 15 years