SOLUTION: Mary is twice as old as Rachel will be in seven years. Four years ago, Mary was four times as old as Rachel. How old is Mary now?

Question 126838: Mary is twice as old as Rachel will be in seven years. Four years ago, Mary was four times as old as Rachel. How old is Mary now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let M = Mary's age now
Let R = Rachel's age now
:
Write an equation for each statement:
:
Mary is twice as old as Rachel will be in seven years.
M = 2(R+7)
:
Four years ago they would be:
(M-4)
(R-4)
:
Four years ago, Mary was four times as old as Rachel.
(M-4) = 4(R-4); just do some basic algebra here
M - 4 = 4R - 16
M = 4R - 16 + 4
M = 4R - 12
Substitute 2(R+7) for M, find R
2(R+7) = 4R - 12
2R + 14 = 4R - 12
2R - 4R = -12 - 14
-2R = -26
R =
R = + 13 yrs is Rachel's age now
:
How old is Mary now?
:
We know that M = 2(R+7); substitute 13 for R
M = 2(13+7)
M = 2(20)
M = 40 yrs is Mary's age now
:
:
Check solutions in the statement:
"Four years ago, Mary was four times as old as Rachel."
(40-4) = 4(13 - 4)
36 = 4(9); confirms our solution
;
;
Did this make sense to you? This is a good method to do all these kind of problems;
First thing, write an equation for each statement. Let the basic operations of
algebra carry you thru. Let me know what you think.
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