Question

a chemist has 12 gallons of alcohol. he draws out 3 gallons and replaces it with water. he draws out 3 gallons of the mixture, again replacing it with water. after five such operations what is the amount of alcohol in gallons left in the mixture

Answer 1

ok first realize that total liquid is always 12 gallons
first time it goes from 12 to 9 , then the ratio of alcohol to water is 9:12 or 3:4
2nd time of the 3 gallons taken out ,3/4 is alcohol or 2.25 gallons leaving 6.75 gal left
3rd time the ratio is 6.75:12 so 3*(6.75/12) or 1.6875 gallons of alcohol are taken out
4th time the ratio is 5.0625:12 ..... 1.265625 gal of alcohol taken out
5th time the ratio is 3.796875:12 .....0.94921875 gal of alcohol taken out

Leaving 2.84765625 gallons of alcohol remaining

Answer 2

a more algebraic approach is to recognize the recursive relationship
X_n+1 = X_n - 3(X_n/12)
X_n+1 = (3/4)X_n

this can be modeled by a geometric sequence
X(n) = 12(3/4)^n

plug in n=5 and you get X = 2.84765625

Answer 3

did that make sense?

Answer 4

yes

Answer 5

how long have you been here?

Answer 6

why tf does he need 12 gallons of alcohol?

Answer 7

its a math question (idk)

Answer 8

@dumbcow, are u still there?

Answer 9

yeah

Answer 10

how long have you been on my question?

Answer 11

i have one more question

Answer 12

oh like 5-10 min, i just happened to come back to this question after awhile

Answer 13

in a certain population the ratio of the number if women to the number in men is 11-10. if the average (arithmetic mean) age of women is 34 and the average age of men s 32, the the average age of the population is A; 32 9/10 b;32 20/21 c; 33 d: 33 1/21 e; 33 1/10

Answer 14

can you help with this one, my good sir?

Answer 15

ok

Answer 16

what grade are u in

Answer 17

im in 5th and in a really advanced class

Answer 18

wow you are really advanced for 5th grade
im already done with school, im a private math tutor so i also help out on this site

Answer 19

thats cool, except you have a really inappropriate picture for your image :)

Answer 20

avg = sum/N

Lets say M is num of men, W is num of women
ratio--> W/M = 11/10 --> W = 11/10M

avgW = sumW/W = 34 --> sumW = 34*(11/10M) = 37.4M
avgM = sumM /M = 32 --> sumM = 32M

avg = (37.4M + 32M)/(M + 11/10M) = 33.05

Answer 21

oh i apologize about the pic, yeah it is inappropriate for young kids

Answer 22

its okay (your image) just that you're a tutor and i wouldnt expect that image :)

Answer 23

thanks for all of you help!

Answer 24

yw

Answer 25

whats your name?