"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

think about it deeply and passionately about this property

i am sorry

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (