You see a rectangle that has been made by putting seven congruent rectangles together. The perimeter of the large rectangle is 114 cm. What is its area?

## Algebra I

## People Triangle: Like, Dislike

Six people who all know each other are in a room. Every two people either like each other or dislike each other. Show that there is a group of three people who either all like each other or all dislike each other.

## Defined Operations 2; Do Composition

If 3 *h* = 10, 7 *h* = 50, 5 *h* = 26; and 4 *b* = 1, 7 *b* = 2.5, 20 *b* = 9, then what is *n*

if *n hb* = 17.5?

## Salary = f(n students)

Many years ago a teacher’s salary was based on the number of students he had. Suppose a salary of $60 per month was to be paid for 50 students and $50 a month for 30 students. If the actual enrollment was 45 students, what should the teacher be paid?

## Given Graphs,Find |f – g|

Suppose that the functions *f(x)* and *g(x)* have the following graphs:

Find the graph which most resembles the graph of |*f(x) – g(x)*|.

## Defined Operation; Find Formula

If 4 → 3, 10 → 6, 7 → 4.5, then what is the formula for *x* → ?

## Defined Operation; Do Inverse

Suppose a linear operation �/� is defined so that:

5 / = 11;

8 / = 17;

12 / = 25.

What is *n* if *n* / = 35?

## Defined Operations 1; Do Composition

Suppose the operations “#” and “*t*” are defined so that:

6 # = 20; 2 # = 4; 10 # = 36; and 5 *t* = 4.5; 10 *t* = 7; 8 *t* = 6.

Then what is *n* if 3 # # *t* = *n*?

## Kite Strings

Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?

## Pet Rocks

The town of Ware has exactly 5000 families. Every family has 0, 1, or 2 pet rocks. Every pet rock belongs to a family. Most families have 1 pet rock. Exactly half of the remaining families have 2 pet rocks. How many pet rocks are there in Ware?