"lito had some marbles. he gave ½ of his marbles plus 1 to felix, ½ of the remaining marbles plus 1 to ces, and ½ of the last remaining marbles plus 1 to pedro. if lito had 1 marble left for himself, how many marbles did he have at first? "

let

x> total amount of marbles at the beginning

we know that

1) He gave ½ of his marbles plus 1 to Felix

(1/2)*x+1=(x+2)/2 (Felix's marbles)

remaining=x-[(x+2)/2]> [2x-x-2]/2> (x-2)/2

2)½ of the remaining marbles plus 1 to Ces

(1/2)*[(x-2)/2]+1=[(x-2)/4]+1> (x+2)/4 (Ce's marbles)

remaining=[(x-2)/2]-[(x+2)/4]> [2x-4-x-2]/4> (x-6)/4

3) ½ of the last remaining marbles plus 1 to Pedro

(1/2)*[ (x-6)/4]+1=[(x-6)/8)+1> (x+2)/8 (Pedro's marbles)

remaining=[(x-6)/4]-[(x+2)/8]> [2x-12-x-2]/8> (x-14)/8

4)If Lito had 1 marble left for himself

so

the last remaining is equal to 1

(x-14)/8=1> x-14=8> x=22 marbles

Verify

(x+2)/2 (Felix's marbles)> (22+2)/2=12

(x+2)/4 (Ce's marbles)> (22+2)/4=6

(x+2)/8 (Pedro's marbles)---> (22+2)/8=3

Lito's marbles> 1

total=12+6+3+1=22> is ok

therefore

the answer is

the total amount of marbles at the beginning was 22