. 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?

Question

jagatuba · Answer

First find your percentages:What percentage of the whole class are girls and what percentage of the class are the boys?

anonymous · Answer

75% girls an 25% boys

jagatuba · Answer

Right. Now the girls averaged 18 points and the boys averaged x points and the whole team averaged 17 points. So what we have to do is make an equation that takes into account the percentages and the averages. 75% and 25% can be written 0.75 and 0.25 respectively. 

Since we know that 0.75+0.25=1, can you think of an equation that we could come up with that can solve for the boys average? don't worry if you can't I will help you.

jagatuba · Answer

The hint was in the way that I put the percentages as an equation equaling 1.

anonymous · Answer

ok so 0.25x=17?

jagatuba · Answer

Close. Maybe if I phrased it differently. If 75% of the class' scored an average of 18 points and 25% of the class scored an average of X then the sum of these two would be 100% of the total class' average of 17.

anonymous · Answer

ok so .75x18+.25x=17?

jagatuba · Answer

Bingo!

jagatuba · Answer

Final answer? (tobe sure you did your math right)

anonymous · Answer

final answer?

jagatuba · Answer

What did you come up with?

anonymous · Answer

14?

jagatuba · Answer

Correct.

anonymous · Answer

so it was just a matter of simplifying

jagatuba · Answer

Yeah. I'm not sure the best way to do this, but I always try to see the big picture first and then see if i can come up with the variables for it. Like in this one: I said to myself first I know that 17 is 100% of the average of the whole class, so what are the variable that make that up. Then it becomes easy. that's just me though. there are certainly other ways to look at it.

anonymous · Answer

ok so how would you do this  A basketball player averaged 20 points a game over the course of six games. His scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?

radar · Answer

|dw:1371942605671:dw|

radar · Answer

did you follow that with understanding?

anonymous · Answer

i think so my understanding was adding all thoes up then that was 108 so 108/6 was 20 but i think i did my math wrong

radar · Answer

You need to add up to 120 for 6 games, 5 scores are given, let x be the sixth score.
The scores must add up to 120 to obtain an average of 20 for the six games.

anonymous · Answer

ok sweet thanks!

radar · Answer

you're welcome, good luck with your studies.