SOLUTION: This is from a worksheet. Mathematics Essentials Grade 8 week 18 pg 52. I think I've got the right answer, but I don't know how to put it into an equation. That is the part I n

Algebra ->  Probability-and-statistics -> SOLUTION: This is from a worksheet. Mathematics Essentials Grade 8 week 18 pg 52. I think I've got the right answer, but I don't know how to put it into an equation. That is the part I n      Log On


   

Question 182649: This is from a worksheet. Mathematics Essentials Grade 8 week 18 pg 52.
I think I've got the right answer, but I don't know how to put it into an equation. That is the part I need help with. Here is the problem:
There are fifty marbles in a sack: red, blue and green. There are ten more green than blue marbles in the sack. The probability of drawing a red or blue marble is one-half. Write and solve an equation to determine how many of each color marble is in the sack.
I figured the answer would be: blue 15, red 10 and green 25. Can you help me determine the equation? And is the answer right?
Found 2 solutions by Mathtut, stanbon:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
I think I've got the right answer, but I don't know how to put it into an equation. That is the part I need help with. Here is the problem:
There are fifty marbles in a sack: red, blue and green. There are ten more green than blue marbles in the sack. The probability of drawing a red or blue marble is one-half. Write and solve an equation to determine how many of each color marble is in the sack.
I figured the answer would be: blue 15, red 10 and green 25. Can you help me determine the equation?
:
let the number of red,blue,and green marbles be r,b,and g consecutively
:
g=b+10..........eq 1
r+b=25..........eq 2---->r=25-b
r+b+g=50........eq 3
:
take r+b's value of 25 from eq 2 and g's value of b+10 from eq 1 and plug those values into eq 3
:
25+b+10=50
:
highlight%28b=15%29number of blue marbles
:
highlight%28r=25-b=25-15=10%29number of red marbles
:
highlight%28g=b%2B10=15%2B10=25%29number of green marbles

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There are fifty marbles in a sack: red, blue and green.
r + b + g = 50
-------------------------------
There are ten more green than blue marbles in the sack.
g = b + 10
--------------------------
The probability of drawing a red or blue marble is one-half.
r + b = 25 or r = 25-b
-----------------------
Write and solve an equation to determine how many of each color marble is in the sack.
---
Substitute for r and g to get an equation in "b":
(25-b) + b + (b+10) = 50
b + 35 = 50
b = 15 (# of blue marbles)
---
Since r = 25-b, r = 10 (# of red marbles)
---------
Since g = b+10, g = 25 (# of green marbles)
----------------------------------------------
blue = 15 ; red = 10 ; green = 25
You have it right.
Cheers,
Stan H.
==============================================
I figured the answer would be: blue 15, red 10 and green 25. Can you help me determine the equation? And is the answer right?