SOLUTION: Grace to her cousin’s age is 4 : 5. 6 years later, the ratio will be 11 : 13.Find Grace’s age.

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Question 861331: Grace to her cousin’s age is 4 : 5. 6 years later, the ratio will be 11 : 13.Find Grace’s age.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = graces age now
Let +c+ = cousin's age now
---------------------------
(1) +g%2Fc+=+4%2F5+
(2) +%28+g+%2B+6+%29+%2F+%28+c+%2B+6+%29+=+11%2F13+
-------------------------------
(2) +13%2A%28+g+%2B+6+%29+=+11%2A%28+c+%2B+6+%29+
(2) +13g+%2B+78+=+11c+%2B+66+
(2) +11c+-+13g+=+12+
----------------------
(1) +5g+=+4c+
(1) +g+=+%28+4%2F5+%29%2Ac+
-------------------
Substitute (1) into (2)
(2) +11c+-+13%2A%284%2F5%29%2Ac+=+12+
(2) +55c+-+52c+=+60+
(2) +3c+=+60+
(2) +c+=+20+
and
(1) +g+=+%28+4%2F5+%29%2A20+
(1) +g+=+16+
Grace is 16
check:
(2) +%28+g+%2B+6+%29+%2F+%28+c+%2B+6+%29+=+11%2F13+
(2) +%28+16+%2B+6+%29+%2F+%28+20+%2B+6+%29+=+11%2F13+
(2) +22+%2F+26+=+11%2F13+
(2) +11%2F13+=+11%2F13+
OK