SOLUTION: There are some green, red and blue buttons in a box. 1/2 of the buttons are green and 1/3 of the buttons are blue. The difference between the number of green and red buttons is 20.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: There are some green, red and blue buttons in a box. 1/2 of the buttons are green and 1/3 of the buttons are blue. The difference between the number of green and red buttons is 20.      Log On


   

Question 1180265: There are some green, red and blue buttons in a box. 1/2 of the buttons are green and 1/3 of the buttons are blue. The difference between the number of green and red buttons is 20.
a) What fraction of the buttons are red?
b) How many buttons are there altogether?
Found 2 solutions by Edwin McCravy, htmentor:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
let n be the number of buttons in the box.

There are some green, red and blue buttons in a box.
G+%2B+R+%2B+B+=+n
1/2 of the buttons are green
G+=+expr%281%2F2%29n
and 1/3 of the buttons are blue.
B+=+expr%281%2F3%29n
The difference between the number of green and red buttons is 20.
G+-+R+=+20
G-20=R
expr%281%2F2%29n-20=R
Substitute for G, R and B in

G+%2B+R+%2B+B+=+n
expr%281%2F2%29n%2B%28expr%281%2F2%29n-20%29%2Bexpr%281%2F3%29n=n 
expr%281%2F2%29n%2Bexpr%281%2F2%29n-20%2Bexpr%281%2F3%29n=n
3n%2B3n-120%2B2n=6n
8n-120=6n
2n=120
n=60


We answer the b) part first:

b) How many buttons are there altogether?
60 buttons altogether.

G+=+expr%281%2F2%29n
G+=+expr%281%2F2%2960
G+=+30

Substitute in 

G-20=R
30-20=R
10=R
a) What fraction of the buttons are red?
IOW, what fraction of 60 buttons is 10 red buttons?

Answer = 10/60 = 1/6

Edwin

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let T = the total number of buttons
Then the number of green = T/2 and the number of blue = T/3
Thus R + T/2 + T/3 = T -> R = T/6
Since G - R = 20 -> T/2 = T/6 + 20 -> T = 60
Therefore, the fraction that are red = 60/6 = 10