There are 3 more red toothpicks than blue toothpicks. A toothpick is chosen at random. Each toothpick is equally likely to be chose. If the probability that a blue toothpick is chosen is 3/7, how many red toothpicks are there and how many blue toothpicks are there?
2007-01-15 08:19:08 · 11 answers · asked by Laretta J 1 in Science & Mathematics ➔ Mathematics
x=blue toothpicks
y=red toothpicks
x= y-3
y= x+3
x/(x + y) = 3/7
x/(x + x + 3) = 3/7
x/(2x + 3) = 3/7
solve for x
x = 3/7(2x + 3)
x= 6/7x + 9/7
7x = 6x + 9
x=9
plug x in above equation
y=9+3
x = 9
y = 12
2007-01-15 08:34:05 · answer #1 · answered by edwarjd 3 · 0⤊ 0⤋
First assign X= number of blue toothpicks. You said that there are 3 more red toothpicks than blue, so let R (red toothpicks)= X (number of blue toothpicks) + 3.
So blue = X
red = 3+X
Now you said chances of picking blue = 3/7
So basically you're saying that X / total number of toothpicks = 3/7).
So divide number of blue toothpicks by the number of red and blue toothpicks which would = 3/7.
So blue (X)/ red (3+X) + blue (X) = 3/7
x/(3+X + X) = 3/7.
Doing the math you get:
X/(3+2X) = 3/7. Now just cross multiply.
7X= 3(3+2X)
7X= 9 + 6X.
And then X= 9! So since you defined X as blue, you have 9 blue toothpicks. And since you defined red as X+3, then you have 12 toothpicks. Now to make sure you got the right answer, ask yourself, does 9/ 9+12 = 3/7? And it does.
2007-01-15 08:31:36 · answer #2 · answered by newhouse 1 · 0⤊ 0⤋
Ok. Blue is 3/7, therefore 3 of every 7 toothpicks are blue, and the other 4 are red.
Since the difference total between red and blue is 3, and the difference is 1 out of every seven, there are 21 total toothpicks - that gives you 9 blue and 12 red (12-9=3)
2007-01-15 08:22:48 · answer #3 · answered by dst3313 3 · 1⤊ 0⤋
# of blue toothpicks is b, # of red is r.
There are 3 more red toothpicks than blue:
r = b + 3
The probability of picking a blue, which is the number of blue toothpicks over the total number of toothpicks, is 3/7:
b/(b + r) = 3/7
Substitute in for r from the previous equation:
b/(b + b + 3) = 3/7
b/(2b + 3) = 3/7
Mulitply both sides by 2b + 3:
b = 3/7(2b + 3) = 6/7b + 9/7
Multiply through by 7 to get rid of fractions:
7b = 6b + 9
Subtract b from both sides:
b = 9
r = 9 + 3 = 12
So there are 9 blue and 12 red toothpicks.
Check: 9/(12 + 9) = 9/21 = 3/7
2007-01-15 08:25:02 · answer #4 · answered by Jim Burnell 6 · 0⤊ 0⤋
9 blue and 12 red
2007-01-15 08:24:31 · answer #5 · answered by Anonymous · 0⤊ 0⤋
B=# of blue
R=# of red
3 + B = R => B = R -3
p(B)=3/7 = B/total
p(R)= 1 - 3/7 = 4/7 = R/total
So,
B/R = 3/4 => (R-3)/R = 3/4
Solve for R: R= 12, so B=9
Thus, R+B= total = 21
Done!
2007-01-15 08:29:18 · answer #6 · answered by Jerry P 6 · 0⤊ 0⤋
2 blue 5 red.
2007-01-15 08:26:27 · answer #7 · answered by kute_regina_gal 4 · 0⤊ 1⤋
four blue and three red. i don't know really, why are you asking this?
2007-01-15 08:23:16 · answer #8 · answered by angela.marie. 3 · 0⤊ 1⤋
why don't you do your own homework
but its 9 just so you know
2007-01-15 08:25:14 · answer #9 · answered by arthur!!! 4 · 0⤊ 0⤋
ya no what i dont even no what the heck u talkin bout! You so effin stupid
2007-01-15 08:23:46 · answer #10 · answered by Josselinne G 1 · 0⤊ 1⤋