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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?

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  1. shadowfiend
    • 5 years ago
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    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?

  2. anonymous
    • 5 years ago
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    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

  3. shadowfiend
    • 5 years ago
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    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.

  4. shadowfiend
    • 5 years ago
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    So we have: pg / g = 18 So how many points were scored in terms of number of girls?

  5. anonymous
    • 5 years ago
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    the girls scored 18....but how do get to the number of boys scored?

  6. shadowfiend
    • 5 years ago
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    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.

  7. shadowfiend
    • 5 years ago
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    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.

  8. shadowfiend
    • 5 years ago
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    So next step, let's split up the fraction: \[\frac{18g + pb}{4b} = \frac{18g}{4b} + \frac{pb}{4b} = 17\]

  9. shadowfiend
    • 5 years ago
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    We also have a way to get b in terms of g -- if g = 3b, then b = g/3. \[\frac{18g}{4\frac{g}{3}} + \frac{pb}{4b} = 17\]

  10. shadowfiend
    • 5 years ago
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    \[\frac{18g}{\frac{4}{3}g} + \frac{pb}{4b} = 17\] \[\frac{18g\cdot 3}{4g} + \frac{pb}{4b} = 17\]

  11. shadowfiend
    • 5 years ago
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    So we now have: \[ \frac{54g}{4g} + \frac{pb}{4b} = 17\]

  12. shadowfiend
    • 5 years ago
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    The g cancels, and we're left with: \[\frac{54}{4} + \frac{pb}{4b} = 17\]

  13. shadowfiend
    • 5 years ago
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    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.

  14. anonymous
    • 5 years ago
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    ok..thanks

  15. shadowfiend
    • 5 years ago
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    \[\frac{pb}{b} = 4(17 - \frac{54}{4}) = 68 - 54 = 14\]

  16. shadowfiend
    • 5 years ago
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    Hope that helped!

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