SOLUTION: A bag contains some silver balls and golden balls. If you remove one silver ball from the bag, 1/7 of the remaining balls in the bag are silver. If you remove 2 GOLDEN balls from t

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Question 1006469: A bag contains some silver balls and golden balls. If you remove one silver ball from the bag, 1/7 of the remaining balls in the bag are silver. If you remove 2 GOLDEN balls from the bag, 1/5 of the remaining balls in the bag are silver. How many balls are there in the bag at first?
Please have a clear explanation, thanks!
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Mathematical model is the system of these two equations:

%28s-1+%2B+g%29%2F7 = s-1,

%28g-2+%2B+s%29%2F5 = s.

where s is the number of silver balls and g is the number of golden balls in the bag initially.

Could you solve it yourself?


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = number of golden balls in bag at first
Let +s+ = number of silver balls in bag at first
+g+%2B+s+ = total number of balls in bag at first
-----------------------------------------
given:
(1) +%28+s-1+%29+%2F+%28+s+-+1+%2B+g+%29+=+1%2F7+
( note that +s+-+1+%2B+g+ are the number of balls remaining in bag )
(2) +s+%2F+%28+s+%2B+g+-+2+%29+=+1%2F5+
( +s+%2B+g+-+2+ are number of balls remaining in bag )
--------------------------
Multiply both sides of (1) by +7%2A%28+s+-+1+%2B+g+%29+
(1) +7s+-+7+=+s+-+1+%2B+g+
(1) +g+-+6s+=+-6+
--------------------
Multiply both sides of (2) by +5%2A%28+s+%2B+g+-+2+%29+
(2) +5s+=+s+%2B+g+-+2+
(2) +g+-+4s+=+2+
------------------
Subtract (1) from (2)
(2) +g+-+4s+=+2+
(1) +-g+%2B+6s+=+6+
-------------------
+2s+=+8+
+s+=+4+
and
(2) +g+-+4s+=+2+
(2) +g+-+4%2A4+=+2+
(2) +g+-+16+=+2+
(2) +g+=+18+
---------------
+4+%2B+18+=+22+
There are 22 balls in the bag at first
-----------------------------
check the answer:
Remove 1 silver ball
There are +4+-+1+=+3+ silver balls left
There are +22+-+1+=+21+ total balls left
+3%2F21+=+1%2F7+
+1%2F7+=+1%2F7+
OK
---------
Remove 2 golden balls
There are +18+-+2+=+16+ golden balls left
There are +4+%2B+16+=+20+ total balls left
+4%2F20+=+1%2F5+
+1%2F5+=+1%2F5+
OK