```Question 126838
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 = {{{(-26)/(-2)}}}
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
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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.```