Algebra Calculation to arrive at a specific number

Question

Taka gave half of his jellybeans to Kiara. Kiara gave half of her jellybeans to Kostas. Kostas gave 1/4 of his jellybeans o Adil and kept the remaining 12. How many jelly beans did Taka originally have?

A. 32

B. 46

C. 68

D. 80

Please explain how the answer is obtained.

Answer 1

Here's an answer without using much algebra.

12 is what remains after Ko gave 1/4 of beans to Ad.

so Ko must have had 12 = 3/4 Ko; Ko = 16

Ki gave 1/2 of her beans to Ko, so Ki must have had 16/(1/2), or 32 beans.

Ta gave half of his/her beans to Ki, so Ta must have had 32/(1/2) originally, or 64 jellybeans.

I agree with Raymond B. There's an error somewhere, either in the answer choices or in the question's values.

Answer 2

When I said "even" when working with answer choices, I meant "whole number".

Answer 3

kl=t/2

t=2kl

ko=kl/2 = t/4

t=2kl=4ko

a=ko/4 = t/16

t=16a= 4ko

after kostas gave 1/4 to adil

kostas had 3/4 of of 1/4 of 3t/16 = 12

48/4 = t/16 = 12

t = 12(16)/3 = 64 for taka originally

kl = 32 for klara

ko= 16 for kostas

a= 4 for adil

half t = 32 for kl

half kl =16 for ko

1/4 ko = 4 for adil leaving 12 for ko

or work backwards, assume A) 32 for t

half goes to kl=16

half goes to ko =8

1/4 goes to a = 2 leaving ko with 8-2 = 6 <12

A) is incorrect

t=46

kl =23

ko = 23/2

a = 23/8

leaving ko with 23/2-23/8 = 11.5 - 2.875 = 8.625 which is less than 12

B) is incorrect

try C)

t =68

kl = 34

ko =17

a = 17/4 leaving ko with 3(17)/4 =51/4 = 12 3/4 which > 12

try D)

t=80

kl=40

ko =20

a =5 leaving ko with 15>12

all the options are wrong. C) is the best answer 68 is close to 64

maybe there's an error in the problem's answers or in the problem

C) is 1st choice. A) is suspiciously half 64, so 2nd choice

B) and D) just flat wrong