Expert: Sherry Wallin - 4/22/2010

Question
QUESTION: The length of a rectangle is four times it's width. If the length is decreased by 12 meters  and the width is increased by 12 meters, the rectangle becomes a square. Find the dimensions of the original rectangle?

ANSWER: Hi Braydon~
    In every word problem the first thing you want to do is to determine what it is you are looking for and then label it with a variable. You also want to see if one unknown quantity is related to another of the unknown quantities. In your problem the length is related to the width with the statement that "the length of a rectangle is four times it's width, so let w =  width of the rectangle, so that the length is 4w. Now you also know that the length is decreased by 12 meters so the new length is 4w-12 while the width is increased by 12 so the new width is w+12. If this rectangle is now a square you know that the length and the width are the same:
4w-12 = w + 12
4w-w-12 = w-w+12
3w-12 = 12
3w-12+12 = 12+ 12
3w = 24
3w/3 = 24/3
w = 8
Now w=8 is the new width but it is the same w you began with so the original width is 8m and the original length is 4w = 4(8) = 32 m.

Math Prof

---------- FOLLOW-UP ----------

QUESTION: A cell-phone company offers a plan of $25 per month and $0.10 per minute of talk. The cost of c dollars, is given by the relation c=25+0.10n, where n represents minutes per month. Each month the company uses the exact air time to calculate the monthly bill.
a) solve the relation for n in terms of c.
b)Create a table of values for this new equation.
c) what is the independent variable? what is the Dependant variable?
d)why might some one rearrange this relation and express it in terms of cost?

Answer
Braydon, please don't use a follow up with a new question, thanks.

To solve an equation in terms of a variable just means to solve it with that variable in it. so to solve the relation for n in terms of c means that you want to solve for n:

c-25 = 25-25+.10n
c-25 = .10n
(c-25)/.10 = .10n/.10
n = (c-25)/.10

A table of values is like an x,y table only here the c is our y and the n is your x:
n          c(n) = 25 + .10n          ordered pair (n,c(n))
0          25 + .10(0) = 25          (0,25)
1          25 + .10(1) = 25.10          (1, 25.10)
2          25 + .10(2) = 25.20          (2, 25.20)   etc

The independent variable is the n and the dependent variable is your c(n)
When n = (c-25)/.10 it is in terms of cost. The value is then that if you want to know how many minutes you can talk for a certain amount of money it is seen directly. For example suppose I only have $35 then I use c = 5 which says I can talk for n = (35-25)/.10 = 10/.10 = 100 minutes

Math Prof