SOLUTION: A box contains red, blue and green pens. If one pen is chosen at random, the probability that a red pen will be chosen is two times the probability for a blue pen and three times

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A box contains red, blue and green pens. If one pen is chosen at random, the probability that a red pen will be chosen is two times the probability for a blue pen and three times       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1189464: A box contains red, blue and green pens. If one pen is chosen at random, the probability that a red pen will be chosen is two times the probability for
a blue pen and three times the probability for a green pen. If there are 12 red pens in the box, how many pens are in the box?
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A box contains red, blue and green pens. If one pen is chosen at random, the probability that a red pen will be chosen is two times the probability for
a blue pen and three times the probability for a green pen. If there are 12 red pens in the box, how many pens are in the box?
~~~~~~~~~~~~~ 

Let x be the number of pens, in total.


Then the probability to get red pen is 12%2Fx;

and two other probabilities are  6%2Fx  and 4%2Fx, according to the problem.


The sum of probabilities is 1, so


    12%2Fx + 6%2Fx + 4%2Fx = 1.


It gives  12 + 6 + 4 = x,  hence,  x = 22 :  there are 22 pens, in all.

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

R = probability of getting red
B = probability of getting blue
G = probability of getting green
These values are between 0 and 1.

We have this given statement
"the probability that a red pen will be chosen is two times the probability for a blue pen and three times the probability for a green pen"

Based on that given info, we can say
R = 2B
R = 3G
We're dealing with the same R value for each equation, so we can equate the two right hand sides
2B = 3G
B = 3G/2
B = 1.5G

Furthermore,
R + B + G = 1
3G + 1.5G + G = 1
5.5G = 1
G = 1/(5.5)
G = 10/55
G = 2/11 is the probability of getting a green pen

B = (3/2)*G
B = (3/2)*(2/11)
B = 3/11 is the probability of getting blue

R = 2B = 2*(3/11) = 6/11
or
R = 3G = 3*(2/11) = 6/11
represents the probability of getting red

If we had 6 red pens out of 11 total, then it would lead directly to 6/11.

Double the values "6 and 11" to get "12 and 22" respectively. This indicates having 12 red pens out of 22 total gives the probability 12/22 = 6/11.
Therefore, it shows that there are 22 pens total in this box.

Answer: 22 pens

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given: There are 12 red pens.

Given: The probability of getting a red pen is twice the probability of getting a blue pen.
Conclusion: The number of blue pens is half the number of red pens -- 6.

Given: The probability of getting a red pen is three times the probability of getting a green pen.
Conclusion: The number of green pens is one-third the number of red pens -- 4.

ANSWER: The total number of pens in the box is 12+6+4 = 22