Over time, science has produce a huge number of standard formulas.
Sometimes these formulas are stated as laws.
A very famous one is:
E is energy.
M is mass.
C is the speed of light.
Energy equals Mass times the speed of light squared.
Back to Algebra for
Adults.
Algebra for Adults:
Part 13, Formulas:
March 3, 2003:
Here are the problems from last time.
15z = 45
z = 45/15 = 3
6a + 16 = 34
6a = 34 - 16
6a = 18
a = 18/6 = 3
c - 35 = 42
c = 42 + 35 = 77
c + 2c - 27 = 3
3c - 27 = 3
3c = 3 + 27
c = 30/3 = 3
7y - 2y = 35
5y = 35
y = 35/5 = 7
Eddie worked 8 hours and earned $120.00.
What was his hourly rate?
Let H represent the hourly rate.
8H = $120.00
H = $120.00/8 = $15.00
Lydia was a advertising actress. She made TV commercials. One 30 second spot she made was very successful. It ran 19,320 times before it was mothballed. Lydia got paid one percent of her union scale for each showing of her film. Her union scale was $235.00 per hour or per appearance, whichever pays more. How much did Lydia earn on that film?
There is a lot of verbiage here. The trick is to extract the
pertinent information.
First we can let E represent Lydia's earnings.
Now, for each time the film was shown, Lydia got one percent of
$235.00.
Since the film was only 30 seconds the hourly rate will be considerably
less than the per appearance rate. You can do the arithmetic to
prove that to yourself if you wish.
The pay for each appearance is .01 x $235.00
Her total income from the spot was 19320 times the pay for each
appearance of the film.
Therefor the equation is:
E = 19320(.01 x $235.00)
Now it is just arithmetic.
E = $45,402.00
Do you believe it?
That's a lot of money for making America dumber.
Now it is time to look at formulas.
What is a formula?
Formally, a formula is a statement or equation of a fact, rule,
or other logical relationship.
What in the world does that mean?
For our purposes now, a formula is just a standardized equation
for a particular kind of situation.
For example:
The standard formula for computing the volume of a cube is
V = LWH
V is the volume of the cube.
L is the length of the cube.
W is the width of the cube.
H is the height of the cube.
Volume equals Length times Width times Height.
Formulas are normally derived and standardized from observation
and measurement.
Over time, science has produce a huge number of standard formulas.
Sometimes these formulas are stated as laws.
A very famous one is:
E is energy.
M is mass.
C is the speed of light.
Energy equals Mass times the speed of light squared.
One formula we use quite often is the one for computing distance
traveled.
D = RT
D is distance traveled.
R is rate of speed.
T is time.
For example:
If we traveled in our auto for three hours at a rate of sixty
miles per hour, how far would we have traveled?
The rate is 60 MPH.
The time is 3 hours.
By formula:
D = 60 x 3 = 180 miles.
If we collected enough empirical data, we could derive this formula.
If we were planning on becoming a scientist we could do that,
but for now we can concentrate on algebra.
Once we have a formula we can manipulate it to solve for other
values.
We call that transforming the formula.
It is really stuff we have already done.
We can apply the rules of equality to do this.
For example:
In the formula V = LWH we can solve for H.
We can use the division rule of equality to do this.
V = LWH
Divide both sides by LW
V/LW = LWH/LW
We see immediately that the LW parts on the right cancel out.
This give us
V/LW = H or in standard form H = V/LW
We can also solve this for L or W using the same procedure.
Okay.
Here are some formulas.
Solve each formula for each of the variables involved.
V = LWH
E = IR
D = RT
s = 26r
C = 6.28r
z = 3a + d
t = 6d - 4
Back to Algebra for Adults.
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