Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem14

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Question number 14, a class of students had a test.  If each boy had gotten three points more on the test, then the average result of the class would have been 1.2 points higher. What percentage of the class are girls?  While it appears at first glance that the information given is not related to the question, let's get started by writing down all the quantities we can gather  and assigning them variables. So let's say that the class average we will need to compute is denoted by A. To do that, we need to know the number of students.  So let's say B denotes the number of boys in the class.  G denotes the number of girls.  And B prime, let that denote the total scores on the boys' exam.  And G prime denotes the points scored by all the girls.  And so now we have an expression for the average given by B prime plus G prime over B plus G. And the new average,  after increasing the scores of the boys,  is given by A plus 1.2.  And that is exactly the old average plus an increase of three points on each of the boys' exams.  The number of students has not changed.  And so we have here an expression for the old average plus 3B over B plus G. Then we subtract A from both sides, write 1.2 as six-fifths.  And we have the equation six-fifths over is equal to 3B over B plus G. And we cross-multiply this.  We have 6B plus 6G is equal to 15B,  which gives us an expression 6G is equal to 9B or two-thirds G is equal to B, which allows us then to consider the class size.  So let's say that S is equal to the class size.  And clearly S is the number of boys plus the number of girls.  But now that's equal to two-thirds G plus G or five-thirds G. And that gives us that the number of girls is related to the class size in the following way.  G is equal to three-fifths of the class size. And three-fifths is the same as 60%. So the answer to question 14 is E, 60.

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