If 9 bags of oats will last 8 horses for 7 days, how long will 6 bags of oats last 5 horses?

## Set 04

## Beef Stroganoff

Beef Stroganoff, well-known underworld figure, is driving ten miles to rendezvous with his associates, Clams Marinara and Froglegs Sautee. It will be necessary for Beef to average 40 mph for the 10 miles in order to make the rendezvous on time. The first 5 miles are in town, and Beef averages 20 mph for those 5 miles. For the second 5 miles, which are in open country, how fast is Beef going to have to drive in order to get there on time? If he is late, his associates will divide up the loot without him.

## Salesman’s Commission

Ormond’s dad Luther sells solar panels. He receives a salary of $400 a week plus 1.2% commission on his sales. If his income last week was $1360, how much were his sales for the week?

## Exponential Equation with 3’s

How many roots are there of the following equation? Find them.

^{2x+2}− 3

^{x+3}− 3

^{x}+ 3 = 0

## Coffee Break

Your boss took everyone to the Java Zone for a coffee break. You sneaked a look at the check and you see that she is paying $15.75 for the three sandwiches, seven cups of coffee, and one piece of pie that were ordered. The next time, the check was exactly $21 for four sandwiches, ten cups of coffee, and one piece of pie.

If you go back by yourself and have one sandwich, one cup of coffee, and one piece of pie, what will you pay?

## Reciprocal Equation

If a non-zero number *N*, diminished by 4 times its reciprocal, equals a given real constant *R*, then in terms of *R*, the sum of all such possible values of *N* is:

- 1/
*R* *R*- 4
- 1/4
- –
*R*

## Cubic Factoring

If *a* ≠ *b*, *a*^{3} – *b*^{3} = 19*x*^{3}, and *a* – *b* = *x*, which of the following conclusions is correct?

*a*= 3*x**a*= 3*x*or*a*= -2*x**a*= -3*x*or*a*= 2*x**a*= 3*x*or*a*= 2*x**a*= 2*x*

## If x + y + z = 1, then …

If *x* + *y* + *z* = 1, show that *xy* + *yz* + *xz* < 0.5.

## Giant Distributive Law = 0

Simplify:

*x*(

*x*(

*x*(2 –

*x*) + 1) +1 ) + 1 +

*x*(

*x*(

*x*(

*x*– 2) + 1) + 1) + 1

This is supposed to come out to be zero. Does it? If not, can you fix it up so that it does?

## Four 4’s: 1 – 20

You are to find expressions for each whole number from 1 through 20, using in each expression exactly four 4�s, plus any mathematical symbols you like: parentheses, plus signs, etc.

Sample: | 1 = | 4 + 4 | . |

4 + 4 | |||