A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. How many points does each boy score on average?
anonymous
 5 years ago
A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. How many points does each boy score on average?

This Question is Closed

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0If there are three times as many girls as boys, that means the number of girls is equal to three times the number of boys. We can express this as g = 3b, where g is for `girls' and b is for `boys'. The girls average 18 points each. This means that the number of points the girls have scored over the number of total girls = 18. If the whole class averages 17 points per person, the number of points the class as a whole scored over the number of total students is 17. Let's say pg is the total points of girls and pc is the total points of the class. We have: pg / g = 18 pc / (g + b) = 17 Do you think with that information that you can solve this?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do I get the numbers to solve the problem...do I assume a class of 100...and if so how do I determine the fraction of girls to boys, to add up to a 100

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0You don't have to assume a class of 100  if you see above, we just put in `g + b'  girls plus boys  which is the total number of people in the class. So pc, the total number of points the class scored, is really pg + pb  points the girls scored + points the boys scored. We want to calculate pb / b  the number of points the boys scored over the number of boys. That means we need two things: the points the boys scored and the number of boys. We can start by calculating the number of points the boys scored.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So we have: pg / g = 18 So how many points were scored in terms of number of girls?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the girls scored 18....but how do get to the number of boys scored?

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0No, the girls scored 18 *on average*. That means the total number that the girls scored is 18g  18 times the total number of girls.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So now we have: (18g + pb) / (4b) = 17 Now we have both things we want to find in here: pb, and b. Remember ultimately we need pb / b  the average number of points each boy scores.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So next step, let's split up the fraction: \[\frac{18g + pb}{4b} = \frac{18g}{4b} + \frac{pb}{4b} = 17\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0We also have a way to get b in terms of g  if g = 3b, then b = g/3. \[\frac{18g}{4\frac{g}{3}} + \frac{pb}{4b} = 17\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{18g}{\frac{4}{3}g} + \frac{pb}{4b} = 17\] \[\frac{18g\cdot 3}{4g} + \frac{pb}{4b} = 17\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So we now have: \[ \frac{54g}{4g} + \frac{pb}{4b} = 17\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0The g cancels, and we're left with: \[\frac{54}{4} + \frac{pb}{4b} = 17\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Remember we're looking for pb / b. We can get that by pulling the 4 away: \[\frac{54}{4} + \frac{1}{4}\frac{pb}{b} = 17\] Then we can solve for pb / b.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{pb}{b} = 4(17  \frac{54}{4}) = 68  54 = 14\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.