SOLUTION: Mary, Melinda and Monica are sisters. The mean age is 12. Mary is 4 years older than Melinda. Monica is 1/2 the age of Mary. How old are they?

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Question 1091997: Mary, Melinda and Monica are sisters. The mean age is 12. Mary is 4 years older than Melinda. Monica is 1/2 the age of Mary. How old are they?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Mary's age now
Let +b+ = Melinda's age now
Let +c+ = Monica's age now
-------------------------------
(1) +%28+a+%2B+b+%2B+c+%29%2F3+=+12+
(2) +a+=+b+%2B+4+
(3) +c+=+%281%2F2%29%2Aa+
-------------------------------
There are 3 equations and 3 unknowns,
so it is solvable
(2) +b+=+a+-+4+
Substitute (2) and (3) into (1)
(1) +%28+a+%2B+a+-+4+%2B+%281%2F2%29%2Aa+%29+%2F+3+=+12+
(1) +%28+5%2F2+%29%2Aa+-+4++=+36+
(1) +5a+-+8+=+72+
(1) +5a+=+80+
(1) +a+=+16+
and
(2) +b+=+a+-+4+
(2) +b+=+16+-+4+
(2) +b+=+12+
and
(3) +c+=+%281%2F2%29%2Aa+
(3) +c+=+%281%2F2%29%2A16+
(3) +c+=+8+
--------------------
Mary is 16
Melinda is 12
Monica is 8
--------------------
check:
(1) +%28+a+%2B+b+%2B+c+%29%2F3+=+12+
(1) +%28+16+%2B+12+%2B+8+%29%2F3++12+
(1) +36%2F3+=+12+
(1) +36+=+36+
OK