SOLUTION: The number of blues was 7 less than the sum or the whites and the greens. The number of greens was 1 greater than the sum of the blues and the whites. How many of each kind were th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The number of blues was 7 less than the sum or the whites and the greens. The number of greens was 1 greater than the sum of the blues and the whites. How many of each kind were th      Log On


   

Question 324538: The number of blues was 7 less than the sum or the whites and the greens. The number of greens was 1 greater than the sum of the blues and the whites. How many of each kind were there if there were three times as many greens as blues?
Answer by vidhyak(98) About Me  (Show Source):
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Let the 3 colors be w,g,b for white, green and blue

The number of blues was 7 less than the sum or the whites and the greens
w + g -7 = b
w + g - b = 7 ...... eq 1

The number of greens was 1 greater than the sum of the blues and the whites
g = 1 + b + w
b + w -g = -1 .........eq 2

three times as many greens as blues
3b = g ------eq 3

Substitute eq 3 in eq 1
w + g - b = 7
w + 3b - b = 7
w + 2b = 7 -------eq 4
Substitute eq 3 in eq 2
b + w - g = -1
b + w - 3b = -1
w - 2b = -1 .........eq5
Add eq4 and eq 5
w + 2b = 7
w - 2b = -1
2w = 6
w = 3

Substitute w = 3 in eq 4 to get the value of b
w + 2b = 7
3 + 2b = 7
2b = 7-3 = 4
b = 2

Substitute w = 3, b = 2 in eq 1 to get the value of g
w + g - b = 7
3 + g - 2 = 7
1 + g = 7
g = 6

There are 3 whites, 2 blues and 6 greens