Question

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?

Answer 1

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?

Answer 2

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

Answer 3

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.

Answer 4

So we have:

pg / g = 18

So how many points were scored in terms of number of girls?

Answer 5

the girls scored 18....but how do get to the number of boys scored?

Answer 6

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.

Answer 7

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.

Answer 8

So next step, let's split up the fraction:

\[\frac{18g + pb}{4b} = \frac{18g}{4b} + \frac{pb}{4b} = 17\]

Answer 9

We also have a way to get b in terms of g -- if g = 3b, then b = g/3.

\[\frac{18g}{4\frac{g}{3}} + \frac{pb}{4b} = 17\]

Answer 10

\[\frac{18g}{\frac{4}{3}g} + \frac{pb}{4b} = 17\]
\[\frac{18g\cdot 3}{4g} + \frac{pb}{4b} = 17\]

Answer 11

So we now have:

\[ \frac{54g}{4g} + \frac{pb}{4b} = 17\]

Answer 12

The g cancels, and we're left with:

\[\frac{54}{4} + \frac{pb}{4b} = 17\]

Answer 13

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.

Answer 14

ok..thanks

Answer 15

\[\frac{pb}{b} = 4(17 - \frac{54}{4}) = 68 - 54 = 14\]

Answer 16

Hope that helped!