SOLUTION: A man and his brother have a combined age of 92 years. 26 years ago, the man was 9 times as old as his brother. How old is the man? How old is the brother

Click here to see ALL problems on Age Word Problems

Question 30059: A man and his brother have a combined age of 92 years. 26 years ago, the man was 9 times as old as his brother. How old is the man? How old is the brother
Found 2 solutions by Paul, sdmmadam@yahoo.com:
Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!
Let the man's age be x
Let his brother's age be y
x+y=92
y=92-x (subsitution)

26 years ago man's age = x-26
26 years ago his bro's age = y-26
Equation:

9(y-26)=x-26
9y-234=x-26
Subsitute:
9(92-x)-234=x-26
828-9x-234=x-26
-9x+594=x-26
-10x=-620
x=62

Hence, the man's age is 62 and his brother's age is 30.
Paul.

Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website!
A man and his brother have a combined age of 92 years. 26 years ago, the man was 9 times as old as his brother. How old is the man? How old is the brother
Let the man be M yrs old and
let the brother be B yrs old.
A man and his brother have a combined age of 92 years.
M +B = 92 ----(1) which gives M =(92-B) ----(*)
26 yrs ago, the man was (M-26) yrs old and
the brother was (B-26) yrs old.
At that time the man was 9 times as old as his brother.
(M-26) = 9(B-26) ----(2)
Using (*) in (2)that is substituting for M,we get
(92-B)-26 =9B - 9X26
92-26+9X26 = 9B+B (grouping like terms,changing sign while changing side)
92+8X26 =10B
92+208 =10B
300 = 10B
B = 300/10 =30
Putting B = 30 in (*),we get
M =92-30 = 62
Answer:The man is now 62 yrs old and his brother is 30 years old
Verification: 26 yrs ago,the man was (62-26) = 36 yrs old and
the brother was (30-26) = 4 yrs old and of course 36 is 9 times 4
Therefore our values are correct.