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Chapter 6

Test Yourself

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Sameer A.

November 5, 2020

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Okay, so this question says on the final exam in a university psychology course, the average arithmetic mean grade was eighty six if the average grades of the M men and that w women in the course for eighty and ninety, respectively. What is the ratio of the number of men to the number of women in the course? So, first of all, we know that for the men, the average was eighty. For the women, the average was ninety and the overall average was eighty six. So because this number eighty six is closer to the women than to men, that automatically means that we have more women which are gonna wait it more towards the women's number for the overall average. So because of that, we know that there's no way that there could be more men so C and D can automatically be eliminated because this wench is that there's three men for every two women and five men for every three women. So we can't have that again because there Cappy more men so that let's go ahead and set up the equation for the average. So we know that if we had score of ninety average for all the women and the square of eighty for all the men. We know that this number can be divided by the total number of women, plus the total number of men, because that's going to determine how many overall people were in the class. And then once we do that, we can get that the average is eighty six again because we're taking the total number of scores for the women and multiplying that by the number of woman and adding that to the total number of men on them, to the score multiplied by the score for the men divided by the total number of people, which is however many women, plus however many men. So then, in order to solve this out, we're going to go ahead and try to get rid of this fraction by multiplying by this w plus, um, on both sides of the equation and the reason why is because then this value and this value will cancel up. Cousin will have ninety w plus eighty men is going to be eighty six w plus. And so now we got rid of our faction, which we don't like fractions, so that At this point, we're going to want to distribute this eighty six to both the women women of the men. Then we get eighty six w plus eighty six men. And then again, this side of the equation stays the same. So then, from here, we're going to try to get all the women on one side of the equation and all the men to the other. Let's take all the women and send them over here and all the men and, well, put that over here so that in order to do that, you have to subtract. Eighty six will be from this side and from this side. And then we're gonna subtract the eighty men from both sides of the equation as well, so that if we did that, then this and this cancels out in this in this cancels out, and then we're left with the ninety women minus the eighty six women is equal to the eighty six men minus eighteen months. So then this simplifies to four w, and this simplifies to six. So we're really close to the answer here. But then let's just took our ratio again. So it says that the ratio off the number of men to women. So we want the men on top. So, men, two women. That means we have to try toe mimic this right here. So to keep the men on the top, we're goingto go ahead, divide women on both sides because then this woman and this woman figure cancels out and then we're left with four is equal to six on over w So we're really close. But then again, we don't want this six on this side. So we're gonna go ahead and divide by the six numbers says of the equation. And again, that's going to cancel out this in this six. Some were left with four over six is equal to men divided by women. And then we just take this faction for over six and we have to simplify that. And we know that the four over six can be simplified by dividing by two top and bottom, so four divided by two, and then the six divided by two. He's going to become too over three. So then we know that for every man that we have for every two men that we have, we're gonna have three women so then are correct. Answer. It's gonna be pretty again. This makes a lot of sense because we know that there has to be more women in the class than men because the overall average means more closer to the women's average, as opposed to the men's average.

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