seven years ago, Mary was 6 times as old as Cora, In 1 year, she will be only twice as old as Cora. Find their present ages

Answer 1

Let:
M=Mary's age now
C=Cora's present age

M-7=6(C-7)
M+1=2(C+1)

M=2C+1
(2C+1)-7=6C-42
2C-6=6C-42
-4C=-36
C=9
therefore Cora's age now is 9 yrs. old
M=2C+1
M=2(9)+C
M=19
therefore Mary's age now is 19 yrs. old.

Answer 2

Using only one variable:

seven years ago:
Cora --- x
Mary --- 6x

present ages:
Cora = x+7
Mary = 6x+7

one year from now
Cora = x+8
Mary = 6x+8

6x+8 = 2(x+8)
6x +8 = 2x+16
4x=8
x =2

present ages:
Cora = x+7 = 9
Mary = 6x+7 = 19