16. Going into his final exam, John has a total of 72 points out of 90 possible in his history class. His final exam is worth 10 points. How many points must he get on his final exam to end the class with an 80%?
8?
17. Joan actually likes 30% of her male friends and 20% of her female friends. She has a total of 200 friends, 45% of them are male. How many female friends does Joan actually like?
22?
Thanks
-MC
Both of your answers are correct.
Thanks!
-MC
16. To find out how many points John needs to get on his final exam to end with an 80% in the class, we first need to calculate the total number of points from the exams he has taken so far.
John has a total of 72 points out of 90 possible points in his history class.
To calculate the current percentage, we divide the points he has by the total possible points and multiply it by 100:
(72 / 90) * 100 = 80%
Since his final exam is worth 10 points, we can subtract the points he already has from the total points required to get 80%:
Total points needed for 80% = 80% * (90 + 10) = 0.8 * 100 = 80
Points he needs to get on his final exam = Total points needed for 80% - Points he already has = 80 - 72 = 8
Therefore, John needs to get 8 points on his final exam to end the class with an 80%.
17. Joan has a total of 200 friends, and 45% of them are male. To calculate the number of male friends, we multiply the total number of friends by the percentage of male friends:
Number of male friends = 45% of 200 = 0.45 * 200 = 90
Since Joan actually likes 30% of her male friends, we can find the number of male friends she likes:
Number of male friends Joan likes = 30% of 90 = 0.30 * 90 = 27
To find out the number of female friends Joan likes, we need to subtract the number of male friends she likes from the total number of friends:
Number of female friends Joan likes = Total number of friends - Number of male friends Joan likes = 200 - 27 = 173
Therefore, Joan actually likes 173 female friends.
For the first question, we can determine how many points John needs to achieve an 80% in the class by setting up an equation:
Let x be the number of points John needs to get on his final exam.
Given that John has a total of 72 points out of 90 possible, we can calculate his current percentage in the class as (72/90) * 100 = 80%.
To calculate the total number of points John will have in the class after the final exam, we add the points he currently has with the points he will earn on the final exam, which gives us 72 + x.
Now, we can set up an equation to solve for x: (72 + x) / 100 * 90 = 80.
To solve this equation, we can cross multiply and simplify: (72 + x) * 90 = 80 * 100.
Expanding, we get 6480 + 90x = 8000.
To isolate x, we subtract 6480 from both sides: 90x = 8000 - 6480.
This simplifies to 90x = 1520.
Finally, we divide both sides by 90: x = 1520 / 90.
By evaluating this expression, we find that x is approximately 16.89.
Therefore, John needs to get approximately 16.89 points on his final exam to end the class with an 80%.
For the second question, we'll use the information provided to calculate the number of female friends Joan actually likes.
Let's denote the number of female friends as F. Since 45% of Joan's friends are male, we can calculate the number of male friends as 45% of the total number of friends, which is 0.45 * 200 = 90.
Given that Joan likes 30% of her male friends, we can calculate the number of male friends she likes as 0.30 * 90 = 27.
We also know that Joan likes 20% of her female friends, so the number of female friends she likes can be found by setting up an expression: 0.20 * F = 27.
To solve for F, we divide both sides of the equation by 0.20: F = 27 / 0.20.
Evaluating this expression, we find that F is equal to 135.
Therefore, Joan actually likes 135 female friends.