Question 1207243
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A money box contained some money at first. A took 1/2 the amount of money and another $1500 from the box. After that, B took 1/4 of the remaining amount of money and another $850 from the box. In the end, C took the rest of the money left in the box. Given that C took $1400, find the amount of money in the box at first.

Let original amount be M
After A took {{{matrix(1,3, (1/2)M, or, (M/2))}}} and another $1,500, amount remaining = {{{matrix(1,3, (1/2)M - "1,500", or, M/2 - "1,500")}}}
After B took {{{matrix(1,3, (1/4)(M/2 - "1,500"), "=", M/8 - 375))}}} and another $850, amount remaining = {{{matrix(4,1, (3/4)(M/2 - "1,500") - 850, 3M/8 - 3(375) - 850, 3M/8 - "1,125" - 850, 3M/8 - "1,975")}}}
Now, with C taking the rest of the money - which happens to be $1,400 - we EQUATE the
2 remainders to get: {{{matrix(3,3, 3M/8 - "1,975", "=", "1,400", 3M/8, "=", "1,400" + "1,975", 3M/8, "=", "3,375")}}}
                             3M = 8(3,375) ----- Cross-multiplying
         Original amount, or {{{highlight_green(matrix(1,7, M, "=", 8("3,375")/3, "=", 8("1,125"), "=", highlight("$9,000")))}}}</pre>