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There were 64 more buttons in box A than box B at first. Ken then added some more buttons in box A. For every 1 button he added to box A, he removed 2 buttons from box B. The number of buttons in box B became 28 fewer than before. In the end, the ratio of the total number of buttons in both boxes to the number of buttons left in box B was 4 : 1. How many buttons were in box A at first?

 Sep 28, 2021
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Let the number of button in box B ==B
Then the number of button in box A==B + 64
Let the number of buttons added to box A==C
Then the number of buttons removed from box B =2C


Now box A  has ==B + 64 + C
And box B now has=B - 2C


B - 2C ==B - 28......................................(1)
[2B - C + 64] / [B - 28] ==4 / 1.............(2), solve for B, C
Solve the 2 simultaneous equations (1) and (2) above.


B ==81   and  C==14
A==81 + 64 ==145 - buttons - what box A had at first.

 Sep 28, 2021

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