Question

"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?"

Answer 1

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