Explanation for Question 31 From the Math (Calc) Section on the Official Sat Practice Test 6
Question 31 reads a group of friends decided to divide the $800 cost of 2 a trip equally among themselves. 3 When two of the friends decided not to go on the trip, 4 those remaining still divided the $800 costs equally, 5 but each friend's share of the cost increased by $20. 6 How many friends were in the group originally? Okay. 7 So for this one, what we're going to want to do is try and 8 convert the sentences, explaining what's going on into mathematical expressions 9 so that we can go forward and solve them. And that's the typical strategy 10 for a word problem. So let's look at this first sentence. 11 A group of friends decided to divide an $800 cost of a trip equally 12 among themselves. So let's define two variables. 13 We have N is equal to number of friends and C is equal to 14 cost per person. So knowing that they decided to divide this 15 $800 costs amongst themselves equally, 16 we can do that $800 divided by the number of friends is equal to 17 the cost per person. 18 Now we're going to consider this second sentence. 19 When two of the friends decided not to go on the trip, 20 those remaining still divided the $800 costs equally, 21 but each friend share of the cost increased by $20. 22 How many friends were in the group originally? 23 So with this, we can set up a second expression. 24 We still have $800 is the total cost, 25 but now it's divided by N minus two. 26 So the initial number of friends minus the two that decided not to go, 27 and now the cost per per...