x / 4 - 8 + 2 x /4 = 19
(1/4 + 2/4) x = 19 +8
(3/4 ) x = 27
x = 27 * 4/3 = 9 * 4 = 36
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For the options A and C, we get 4(4x - 3) - 6x = 10 x -12
so we get 10x = 10 x this is true for any value of x.
But for B and D, we get 4(4x - 3) - 6x = 9x - 12 => x = 0
4(4x - 3) - 6x = 8 x - 12 => x = 0
there is one solution, x =0 for B and D.
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Difference between the balances in the two accounts at the beginning :
= $ 260 - $ 140 = $ 120
Difference in the deposit amount = $ 150 - $ 120 = $ 30
So the difference in balances reduces by $ 30 each month. So it will take $120/$30 = 4 months to even out.
Alternate method
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Balance in David's account after x months = $ 140 + $ 150 * x
Balance in Louis acount after x months = $ 260 + $120 * x
$ 140 + $ 150 * x = $ 260 + $120 * x
$ (150 - $120) x = $260 - $ 140
30 * x = 120
x = 4
