<p>To solve basic group problems, isn't the formula
Group1 + Group2 - Both + Neither = Total?</p>
<p>Second, I don't want to break any CC rules, but there was a math question on the last SAT that I guessed on and think I got right, but don't know why. It said something like "9 kids are on the Science Bowl, 10 are on the Math Team, 11 are on only one team. How many are on both?" People say to use a Venn diagram, but I'm not quite sure how. Also, the above formula doesn't seem to work here. Thanks.</p>
<p>Let's make up a problem so we don't mess with anything. 5 are taking Spanish, 6 are taking French, 7 are only taking one class. How many are in both? I don't think the above formula works because you don't know the total # of students. Therefore, you hand-distribute the people such as there are 7 on the 'only one class' side of the chart.
Spanish French Total
Only 1: 3 4 7
Both: 3 3 3
Total: 6 7<br>
Notice how you have to give French one additional person to balance out the totals for each class. Therefore, 3 people are taking both classes.</p>
<p>I don't understand your chart. 5 are taking Spanish and 6 French, but on your chart 6 are in Spanish and 7 in French.</p>
<p>Also, for this particular type of problem, doesn't Total = Group 1 + Group 2 - Both? The problem doesn't mention people who are in neither group. There's obviously a simple way to do this, there always is. I'm just not seeing it.</p>
<p>Let's find out why. Let n be the number who are taking both Spanish and French. So 5-n students are only taking Spanish and 6-n students are only taking French. Therefore, the total T would be</p>
<p>T = (5-n) + (6-n) + n = 5 + 6 - n or G1 + G2 - Both.</p>
<p>But in this problem we have two unknown variables, T and both. I'm not sure which one you intend to solve for, so I'll do both of them - </p>
<p>We can solve for the number of students who are taking both French and Spanish like so: The number of students taking only one class is 7. If the number taking both classes is n, we can set up an equation like so:</p>
<p>(5-n) + (6-n) = 7
n = 2.</p>
<p>We can now solve for the total number of students using the above formula:</p>
<p>T = 5 + 6 - 2 = 9,</p>
<p>or we can do it by simply adding up the three groups of students:</p>
<p>T = 3 (taking only Spanish) + 4 (taking only French) + 2 (taking both) = 9.</p>
<p>Hope this helps.</p>
<p>*The way I solved these assumed that every student is taking at least one class. If the problem told you how many students were taking neither, then you would just add that number to the previous total to get the final total.</p>
<p>Whoops, I messed up the 'both' column of the chart. It should look like: </p>
<p>
Spanish French Total
Only 1: 3 4 7
Both: 2 2 2
Total: 5 6 9
So it is basically the same thing as the algebraic method, 2 students are taking both classes, and there are a total of 9 students taking either class. Total = Group 1 + Group 2 - both.</p>
<p>wait i dont get it after minutes of scrutinizing this. ajwchin can you please be more specific( i know thats not possible, but please try- - im slow)</p>
<p>Because 7 is not the total. If we knew what the total was (we later find out it is 9), then I could say that</p>
<p>T = (5-n) + (6-n) + n = 9, which is the formula that we came up with in the beginning.</p>
<p>However I am setting it equal to the number of people that only take one class, which is 7. Let's think about this: If I add the number of people that only take Spanish to the number of people that only take French, then I should get the total number that only take one class, right? Well, what is the number of people that only take Spanish? Well, it is the total number of people that take Spanish, minus the number of people that take both classes, or (5-n). Same thing with French, so it is (6-n). So we can now set up this equation:</p>
<p>(5-n) + (6-n) = 7, and solve for n to get the number of people that are taking both classes. Note that this equation looks very similar to the one involving total (T), but is actually quite unrelated (for our purposes). I think that was where you were getting confused.</p>
<p>Also, I arbitrarily picked the letter n. You could use x like they did, or any other letter.</p>
<p>^ That's weird. If that's true, SAT II Math for Dummies, where I got the formula from, completely screwed up on a section. Timmy's answer confirms his formula, but I can't see a test book making the same mistake over and over (4 times over 2 pages). Let's confirm it with a problem from the Dummies book. If their answer is right, I'm confused. If not, then they gave the wrong formula. Here's the problem:</p>
<p>The charter academy has exactly 110 students. 47 students are enrolled in PE, while 56 students are enrolled in Drivers Ed. 33 are enrolled in both. How many students are not enrolled in either class?</p>
<p>Their method: 110 = 47 + 56 + Neither Group - 33 = 110. This yields 40. It seems right.</p>
<p>I think the difference in formulas has to do with the fact that the SAT problem is dealing with people only in one group, while the Dummies problem doesn't. That's why the 2*Both is necessary on the SAT problem, while not necessary on the charter academy problem..</p>