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Question 147671: A man and his brother have a combined age of 164 years. 46 years ago, the man was 7 times as old as his brother. How old is the man? How old is the brother?: A man and his brother have a combined age of 164 years. 46 years ago, the man was 7 times as old as his brother. How old is the man? How old is the brother?
Answer by scott8148(2420) About Me  (Show Source):
You can put this solution on YOUR website!
"A man and his brother have a combined age of 164 years" __ m+b=164 __ subtracting b __ m=164-b

"46 years ago, the man was 7 times as old as his brother" __ m-46=7(b-46) __ distributing __ m-46=7b-322

substituting __ (164-b)-46=7b-322 __ 118-b=7b-322 __ adding b+322 __ 440=8b __ dividing by 8 __ 55=b

substituting __ m=164-(55) __ m=109
Question 147671: A man and his brother have a combined age of 164 years. 46 years ago, the man was 7 times as old as his brother. How old is the man? How old is the brother?: A man and his brother have a combined age of 164 years. 46 years ago, the man was 7 times as old as his brother. How old is the man? How old is the brother?
Answer by Fombitz(1152) About Me  (Show Source):
You can put this solution on YOUR website!
Man's age is M.
Brother's age is B.
1.M+B=164
46 years ago the man's age was M-46.
46 years ago his brother age was B-46.
2.M-46=7(B-46)
We can use eq. 1 to solve for M in terms of B.
Then substitute this into eq. 2.
1.M+B=164
M=164-B
Now substitute.
2.M-46=7(B-46)
(164-B)-46=7(B-46)
118-B=7B-322
-8B=-440
B=55
Then from eq. 1,
M=164-B
M=164-55
M=109
The man is 109 years old and his brother is 55.