Question 1184417: A factory manufactures three types of golf balls: Eagle, Birdie, and Bogey. The daily production is 10,000 balls. The number of Eagle and Birdie balls combined equals the number of Bogey balls produced. If the factory makes three times more Birdie than Eagle balls, find the daily production of each type of ball.
Answer by greenestamps(13198)   (Show Source):
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"The number of Eagle and Birdie balls combined equals the number of Bogey balls produced"
That means half of the 10,000 balls are Bogey balls. So 5000 Bogey balls.
"the factory makes three times more Birdie than Eagle balls"
The statement of a math problem should never use that language, because it doesn't mean what most people think it means.
If one number is x and a second number is three times AS GREAT AS the first, then clearly the second number is 3 times x, or 3x.
But if one number is x and a second number is three times GREATER THAN x, then the second number is the first number, plus that number three MORE times -- x+3x=4x.
Unfortunately, in sloppy everyday usage, "3 times as great as" and "3 times greater than" are used to mean the same thing.
So in this case we don't really know whether the ratio of Eagle to Birdie balls is 1:3 or 1:4. In many badly written problems like this, you can tell which is the intended meaning, because only one of the meanings leads to answers that are whole numbers. But in this case both meanings do -- so we can't know what the intended answer is.
Correct answer: x Eagle balls and 4x Birdie balls; 5000 total; so 1000 Eagle balls and 4000 Birdie balls.
Incorrect answer (but very likely the intended one): x Eagle balls and 3x Birdie balls; 5000 total; so 1250 Eagle balls and 3750 Birdie balls.
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