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Question 67217This question is from textbook Advanced mathematics
: The ratio of greens to blues was 2 to 1, and twice the sum of the number of blues and the number of whites exceeded the number of greens by 10. If there were 35 blues, greens, and whites in all, how many were there of each color?
This question is from textbook Advanced mathematics
Found 2 solutions by stanbon, BobbyDamiano:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The ratio of greens to blues was 2 to 1, and twice the sum of the number of blues and the number of whites exceeded the number of greens by 10. If there were 35 blues, greens, and whites in all, how many were there of each color?
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Let number of blues be x
Then number of greens is 2x
And number of whites is 35-3x
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EQUATION:
2(x+35-3x)=2x+10
-4x+75=2x+10
6x=65
This does not turn out to be a whole number.
Check your problem statement.
Cheers,
Stan H.
Answer by BobbyDamiano(3)  (Show Source):
You can put this solution on YOUR website! Translation:
The ratio of greens to blues was 2 to 1; G / B = 2 / 1 (Cross Multiply)
This becomes G = 2B (1st Equation)
Twice the sum of the number of blues and the number of whites exceeded the number of greens by 10.
2 (B + W) = G + 10 (2nd Equation)
If there were 35 blues, greens, and whites in all,
The final equation is: B + G + W = 35
Multiplying 2 (B + W) = G + 10 it becomes, 2B + 2W = G + 10
Replace: G from the first equation, in the final equation:
B + 2B + W = 35
3B + W = 35
2B + 2W = 2B + 10 (Replacing the G with 2B)
Merging the two equations together we get:
2B + 2W = 2B + 10 (cancelling 2B from both sides)
B + 2B + W = 35 (add B to 2B)
2W = 10, we get the first answer for W which is 5.
Using 5 we put it in the second equation:
3B + 5 = 35
3B = 30, we get the second answer for B which is 10.
To find G, we simply use the first equation:
G = 2(10) (B is 10)
G is 20.
Using all the variables in the last equation we get:
B (10) + G (20) + W (5) = 35
10 + 20 + 5 = 35. SOLVED!
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