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:
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 = + 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.