When Bruce started bowling, he won 1/4 of the games he played. Within six months, he was winning 7/16 of his games. If he improves at the same rate, what fraction of his games should he expect to win after another six months?
I subtracted the 1/4 from 7/16 and came up with 3/16 for the first 6 months. Then I added the 7/16 for the next 6 months and came up with 10/16 or 5/8. I know this is not correct.
What am I doing wrong?
While there may be more than one interpretation of what "the same rate" means, under the most reasonable interpretation I get the same answer you got (5/8).
Which leads me to ask, why do you say that you "know this is not correct"? Do you have an answer key that gives a differing answer?
No, I don't. I just didn't think you should subtract the 1/4 from the first 6 months.
When bruce started bowling, he won 1/4 of the games he played. Within six months, he was winning 7/16 of his games. If he improves at the same rate, what fraction of his games should he expect to win after another six months?
I REALLY need to know the answer.. So anyone actually KNOW the answer?
Plz
To solve this problem, let's break it down step by step.
First, let's re-evaluate the calculation you made - subtracting 1/4 from 7/16 and getting 3/16. This step is incorrect because we cannot directly subtract fractions with different denominators. To subtract fractions, we need to have a common denominator.
To find a common denominator, we need to find the least common multiple (LCM) of the denominators. In this case, the denominators are 4 and 16. The LCM of 4 and 16 is 16. Now, we can convert the fractions to have a common denominator of 16:
1/4 = 4/16
7/16 remains the same.
Now, let's subtract 4/16 from 7/16:
7/16 - 4/16 = 3/16
So, your calculation of 3/16 is indeed correct for the improvement made in the first 6 months.
Next, we want to find out what fraction of games Bruce should expect to win after another 6 months. To do this, we need to determine the new fraction of games won by Bruce in the second 6-month period.
One way to think about it is to consider the improvement made in the first 6 months as a fraction of the remaining games. Since Bruce won 3/16 of the games in the first 6 months, he has 13/16 of the games left to play.
Now, we want to find out what fraction of these remaining 13/16 games Bruce would win in the next 6 months. If he improves at the same rate as before, then the fraction of games won should remain the same. Therefore, after another 6 months, Bruce should expect to win 3/16 of the remaining 13/16 games.
To calculate this, multiply the fractions:
(3/16) * (13/16)
Multiply the numerators to get the new numerator:
3 * 13 = 39
Multiply the denominators to get the new denominator:
16 * 16 = 256
So, after another 6 months, Bruce should expect to win 39/256 of his remaining games.
Therefore, the correct answer is 39/256.