Would you please explain the solution to Problem #31 in the calculator-allowed section of Practice Test #6?

This one is all about translating carefully between words and math. You can write two equations. Let’s use for the original number of friends. If all friends go on the trip, the cost per person is $20 less than if friends go on the trip. Cost per Person with Friends minus Cost per Person with Friends is $20.

To solve, multiply by :

That tells you that the number of friends originally in the group is either 10 or –8. Since the answer can’t be negative, it must be 10.

BONUS: The other way to go on this one is the way I actually did it the first time: just dividing 800 by a bunch of numbers in a row until I saw a difference of 20:

800/4 = 200

800/5 = 160

800/6 = 133.333

800/7 = 114.286

**800/8 = 100**

800/9 = 88.889

**800/10 = 80**

There you have it: 100 and 80 are 20 apart, and that’s the difference between splitting 800 over 10 people vs. over 8 people. That was fast!