anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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shadowfiend
  • shadowfiend
If 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
  • anonymous
how 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
  • shadowfiend
You 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.

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shadowfiend
  • shadowfiend
So we have: pg / g = 18 So how many points were scored in terms of number of girls?
anonymous
  • anonymous
the girls scored 18....but how do get to the number of boys scored?
shadowfiend
  • shadowfiend
No, 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
  • shadowfiend
So 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
  • shadowfiend
So next step, let's split up the fraction: \[\frac{18g + pb}{4b} = \frac{18g}{4b} + \frac{pb}{4b} = 17\]
shadowfiend
  • shadowfiend
We 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
  • shadowfiend
\[\frac{18g}{\frac{4}{3}g} + \frac{pb}{4b} = 17\] \[\frac{18g\cdot 3}{4g} + \frac{pb}{4b} = 17\]
shadowfiend
  • shadowfiend
So we now have: \[ \frac{54g}{4g} + \frac{pb}{4b} = 17\]
shadowfiend
  • shadowfiend
The g cancels, and we're left with: \[\frac{54}{4} + \frac{pb}{4b} = 17\]
shadowfiend
  • shadowfiend
Remember 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.
anonymous
  • anonymous
ok..thanks
shadowfiend
  • shadowfiend
\[\frac{pb}{b} = 4(17 - \frac{54}{4}) = 68 - 54 = 14\]
shadowfiend
  • shadowfiend
Hope that helped!

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