SOLUTION: In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? 1. 13 2. 7 3. 25 4. 20

Algebra ->  Probability-and-statistics -> SOLUTION: In a bag containing only blue, red and green marbles, all but 15 are blue, all but 13 are red and all but 12 are green. How many are red? 1. 13 2. 7 3. 25 4. 20      Log On


   

Question 636706: In a bag containing only blue, red and green marbles, all but 15 are blue, all but
13 are red and all but 12 are green. How many are red?
1. 13
2. 7
3. 25
4. 20
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of red marbles be r .
Let the number of green marbles be g .
Let the number of blue marbles be b .
All the marbles means r%2Bb%2Bg marbles.
The fact that all but 15 of the marbles are blue means that
r%2Bg=15 (15 of those marbles are either red or green).
The fact that all but 13 of the marbles are red means that
g%2Bb=13 .
The fact that all but 12 of the marbles are green means that
r%2Bb=12 .
We have a system of 3 linear equations with 3 variables:
system%28r%2Bg=15%2Cg%2Bb=13%2Cr%2Bb=12%29
Subtracting the second equation from the first, we get
r%2Bg-%28g%2Bb%29=15-13 --> r%2Bg-g-b=2 --> r-b=2
Adding that to the third equation we get
r%2Bb%2B%28r-b%29=12%2B2 --> r%2Bb%2Br-b=14 --> 2r=14 --> 2r%2F2=14%2F2 --> highlight%28r=7%29