SOLUTION: Esther is 18 years younger than her mother. If the sum of their ages 2 years ago was 70.How old is Esther and her mother.

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Question 831018: Esther is 18 years younger than her mother. If the sum of their ages 2 years ago was 70.How old is Esther and her mother.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +e+ = Esther's age now
Let +m+ = her mother's age now
--------------
(1) +e+=+m+-+18+
(2) +%28+e-2+%29+%2B+%28+m-2+%29+=+70+
--------------------------
(1) +-e+%2B+m+=+18+
and
(2) +e+%2B+m+-+4+=+70+
(2) +e+%2B+m+=+74+
----------------------
Add (1) and (2)
(1) +-e+%2B+m+=+18+
(2) +e+%2B+m+=+74+
+2m+=+92+
+m+=+46+
and, since
(1) +e+=+m+-+18+
(1) +e+=+46+-+18+
(1) +e+=+28+
Esther is 28 and her mother is 46
check:
(2) +%28+e-2+%29+%2B+%28+m-2+%29+=+70+
(2) +%28+28-2+%29+%2B+%28+46-2+%29+=+70+
(2) +26+%2B+44+=+70+
(2) +70+=+70+
OK