<p>3) This is the easy way, without having to do algebra (except some factoring). First, find all the combinations of how many people and how many slices they get. You should see that there are 60 slices, and 60 is divisible by 2,3,4,5,6,10,12,15,20,30. You should see that it can’t be 2,3, or 4 because if you subtract 4 people from them, then you have 0 or a negative. So you can get rid of 2,3 and 4, as well as their pair which would equal 60 (12, 20, 30). So your left with 4 combinations: either there are 5 people that get 12 slices; 12 people that get 5 slices; 6 people that get 10 slices, or 10 people that get 6 slices. So then you test each one to see which one is right. For example, I’ll start with 10 people that get 6 slices. You subtract 4 people who do not want pizza, to get 6 people that each get 10 slices. You see that this is correct (each person would get 4 more slices). So you know there are 10 people. Then you just factor each of the answers and get that the correct answer is A.</p>
<p>This explanation seems long, but in reality, the problem takes around a minute.</p>
<p>4) When I come across questions like these, I tend to like to have real numbers. So let’s just say there are 10 boys in the class. With there being 3/4 the amount of girls as boys in the class, it comes out to 7.5 girls. 1/2 of the boys speak French, so 5 speak French. 2/3 of the girls speak French, so 5 girls speak French. So you have 10 out of the class of 17.5 that speak French. 10/17.5 = 4/7</p>
<p>5) When 10 people shoot an average of 75, that means 750 total baskets were made. When 8 people shoot an average of 79, that means 632 total baskets were made. So when 2 people were taken out, 750 - 632= 118 baskets were also gone. Since the highest amount of baskets possible is 100, 118- 100 = 18 baskets is the lowest.</p>
<p>6) Let’s say the average of the 3 angles that are not Z equal the variable x. From there, you can derive the equation 2x + 10 = z. You can also find an equation using the total degrees of the quadrilateral. Because the average is x, the total degrees of the 3 angles is 3x. So if you add 3x (the total degrees of angels W, X, and Y) with the degreese of angle Z (which is 2x + 10) you have the total degrees of the quadrilateral.</p>
<p>So 3x + 2x + 10 = 360. Solve for x and you get 70. So the average of W,X and Y is 70, so the total degrees of W,X, and Y is 210. So Z = 360 - 210 =150.</p>
