Question 1208344
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Hi
Alan Ben and Caleb shared some marbles. Alan took 40% of the marbles and was given 1 more . Ben took 25% of the remaining and was given 3 more. Caleb took the remaining 12 marbles. How many were there at first.

Let original number of marbles, be M
Then Alan took 40%(M) = .4M, and given 1 more, ended up with .4M + 1
After Alan's .4M + 1, number remaining = (M - .4M) - 1 = .6M - 1
With Ben taking 25% of remainder, given 3 more, he ended up .25(.6M - 1) + 3 
Number remaining after Ben's take: (1 - .25)(.6M - 1) - 3
                                         .75(.6M - 1) - 3
                                           .45M - .75 - 3 = .45M - 3.75
Since Caleb took the remainder (.45M - 3.75), which was 12, we get: .45M - 3.75 = 12
                                                                           .45M = 15.75 
                                        <font size = 4><font color = red><b>Original number of marbles</font></font></b>, or {{{highlight_green(matrix(1,7, M, "=", 15.75/.45, "=", "1,575"/45, "=", highlight(highlight(35))))}}}</pre>