Question 1108453: A is 2 years older than B, B is three years older than C and the sum of their ages is half the age of D. At the end of 10 years' time, the sum of the ages of A, B and C will be equal to the age of D. Find their present ages
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A is 2 years older than B,
A = B + 2
B is three years older than C
B = C + 3
or
C = B - 3
and the sum of their ages is half the age of D.
A + B + C = .5D
At the end of 10 years' time, the sum of the ages of A, B and C will be equal to the age of D.
(A+10) + (B+10) + (C+10) = D + 10
A + B + C + 30 = D + 10
A + B + C = D + 10 - 30
A + B + C = D - 20
Subtract the 1st equation
A + B + C = D - 20
A + B + C = .5D
--------------------Subtraction eliminates ABC, find D
0 = .5D - 20
20 = .5D
D = 40 yrs is D's age
:
using the equation A + B + C = .5(40), replace A with (B+2) and C with (B-3)
(B+2) + B + (B-3) = 20
3B - 1 = 20
3B = 21
B = 7 yrs is B's age
Find A
A = B + 2
A = 9 yrs is A's age
Find C
C = B - 3
C = 4 yrs is C's age
:
Find their present ages: 9, 7, 4, 40
:
Check these solutions in the statement
"At the end of 10 years' time, the sum of the ages of A, B and C will be equal to the age of D."
|
|
|
