SOLUTION: Six years ago, Albert was 1/5 as old as his mother. His mother is now 3 times as old as Albert. how old is his mother?

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Question 1004818: Six years ago, Albert was 1/5 as old as his mother. His mother is now 3 times as old as Albert. how old is his mother?
Found 2 solutions by fcabanski, josmiceli:
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Albert is A years old. Mom is M years old.


Six years ago: A = M/5


Now: 3*(A+6) = M+6


Substitute M/5 for A in the second equation.


3*(M/5 + 6) = M+6
3M/5 + 18 = M+6
12 = M - 3M/5 = 5M/5 - 3M/5 = 2M/5


60 = 2M


30 = M


The question asks how old is Albert's mom. Remember, we called M her age 6 years ago. So now her age is 30+6 = 36.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Albert's age now
+a+-+6+ = Albert's age 6 yrs ago
Let +m+ = his mother's age now
+m+-+6+ = his mother's age 6 yrs ago
----------------------------------
(1) +a+-+6+=+%281%2F5%29%2A%28+m+-+6+%29+
(2) +m+=+3a+
----------------
(2) +a+=+m%2F3+
Substitute (2) into (1)
(1) +m%2F3+-+6+=+%281%2F5%29%2A%28+m+-+6+%29+
(1) +m+-+18+=+%283%2F5%29%2A%28+m-6+%29+
(1) +5m+-+90+=+3m+-+18+
(1) +2m+=+72+
(1) +m+=+36+
His mother is 36
----------------
check:
(2) +a+=+m%2F3+
(2) +a+=+36%2F3+
(2) +a+=+12+
and
(1) +a+-+6+=+%281%2F5%29%2A%28+m+-+6+%29+
(1) +a+-+6+=+%281%2F5%29%2A%2836+-+6+%29+
(1) +a+-+6+=+%281%2F5%29%2A30+
(1) +a+-+6+=+6+
(1) +a+=+12+
OK