Chapter 2-5

We learned about equations and problem solving on Friday.

Define the variable in terms of one another.
You define the thing you are looking for in a variable in relation to the information you already have.

For example,

The length of the rectangle is 6in. more than its width. The perimeter of the
rectangle is 24 in. What is the length of the rectangle?

What are we finding and what is the relation? (Relate)
We're finding the length. The length is 6 in. more than the width.

Now define the variable.
w: width and w+6: length.

Solve (Write)
p=2L+2w
24=2(w+6)+2w.
24=2w+12+2w
24=4w+12
24-12=4w+12-12
12=4w
12/4=4w/4
3=w
The width is 3in. The length is 6in. more than the width, so the length is 9in.

Consecutive Integer Problem

You can find consecutive numbers adding up to a number by the "defining variable in terms of another" way.

For example,

The sum of tree consecutive integers is 147. Find the integers.

Define
n= the first integer
n+1= the second integer
n+2= the third integer

Relate
1st integer plus 2nd integer plus third integer

Write
n + n+1 + n+2 =147
n+n+1+n+2=147
3n+3=147
3n+3 -3=147 -3
3n=144
3n/3=144/3
n=48