Using Formulas
3.4 p. 143
Using Formulas to Solve Problems
A formula is an equation that shows a
relationship between values that are
represented by variables.
The formula, d = rt, shows a relation between
the distance traveled, the rate of speed, and
the time traveled at this rate of speed.
Our objective is to apply formulas to solve
problems!
Example Problem p. 143
Suppose you travel 162 miles in 3 hours. We have to go back to the
familiar process of WRITE, SUBSTITUTE, and SOLVE.
Write the formula that applies to the problem
d = rt
Substitute the info we have.
162 = r (3)
Solve, using equality properties
162 = 3r
3
3
54 = r
The rate of speed was 54 mph.
You must follow the rules for calculator lessons.
These are: WRITE each step BEFORE solving
Show all steps
Label all work
When you see this calculator, it means
you are allowed to use a calculator
on the problem.
The Distance Formula
If you drove for 9 ¾ hours and
traveled a total of 273 miles, how fast were
you going?
d = rt
distance = rate of speed(time)
Write
273 = (r)9.75
Substitute what you have.
273 = (r) 9.75
9.75 9.75
Solve
28 mph=rate of speed
The Cricket Problem p. 143
F=
F=
n + 37
4
96
4
+ 37
F = 24
F = 61o
+ 37
Someone with way too much
time on their hands found
they could estimate the
temperature by counting
the frequency of cricket
chirps.
If a cricket was chirping about 96 times per
minute, you could find the temperature by
substituting and solving this formula.
If a cricket was chirping about 96 times per
minute, I would step on it.
Perimeter Formulas
Perimeter is the distance around a shape.
Rectangular perimeter can be found by these formulas:
P = 2l + 2w
or
P = 2(l + w)
PLEASE notice that the first one is
just the second one
after the 2 has been
distributed!!
P = 2(18.5) + 2(12.5)
P = 2(18.5 + 12.5)
P = 37 + 25
P = 2(31)
12.5 ft.
P = 62 ft.
P = 62 ft.
18.5 ft.
Perimeter Formulas
Perimeter is the distance around a shape.
Rectangular perimeter can be found by these formulas:
P = 2l + 2w
P = 2(27.3) + 2(16.8)
P = 54.6 + 33.6
P = 88.2 cm
or
Choose which formula
you want..
Follow the complete process
P = 2(17.4) + 2(8.6)
P = 2(27.3 + 16.8)
P = 2(44.1)
P = 88.2 cm
P = 2(17.4 + 8.6)
P = 2(26)
P = 34.8 + 17.2
P = 52 ft.
P = 2(l + w)
Would you
ever use this?
P = 52 ft.
Formula Practice
p. 145 (Even 2-16)
2) d = rt
2730 = r (9.75 )
___________
9.75
9.75
Notice how you
can manipulate
the formula
to find each part.
280 mph= r
d = rt
To find the distance, we
would just multiply
the rate(time).
d = rt
d = rt
r r
To find the time,
We would divide both
sides by the rate.
4) d = r t
10.2
ft = .5ft (t)
_______________
.5
.5
20.4 hours = time
n
8) F =
+ 37
4
F = 64 + 37
4
F = 16 + 37
F = 53 degrees
6) F =
n + 37
4
F = 80 + 37
4
F = 20 + 37
F = 57 degrees
10) P = 2(l + w)
P = 2( 7.3 + 6.2)
P = 2( 13.5)
P = 27 m
14) F = 1.8C + 32
F = 1.8(56) + 32
F = 100.8 + 32
F = 132.8
F = 1.8C + 32
Now that the cricket is dead we will use a
formula to convert C to F.
12)
F = 1.8C + 32
F = 1.8(-4) + 32
F = -7.2 + 32
F = 24.8
Challenge
There is a type of formula that is very similar to
the distance formula. It’s called the work
formula.
Work completed = rate of work (time)
We will work two examples of these problems.
Keep an open mind……
Frank can cut a lawn in 2 hours.
His brother Jeff can cut the same lawn in 3 hours.
How long will it take them if they cut the lawn at the same time?
We are asked to find the time, in hours, it will take both people to finish
the lawn.
Since we are looking for time in hours, Frank can cut ½ the yard in an
hour and Jeff can cut 1/3 the yard in an hour.
The “pipe problems” are problems you will see quite often in algebra……
One pipe can fill a tank in 5 hours. Another pipe can fill the same
tank in 3 hours. How long will it take to fill the tank with both pipes?
Oh, no!!!! Only the pipe that
fills the tank in 3 hours is working!
On top of that, the drain is open.
The drain can let all the water out in
9 hours. How long will it take
to fill the tank now??????
What Did We Accomplish?
• Did you use formulas to solve problems?
• Hopefully, you remembered to follow the
process of write, substitute, and solve.
• Hopefully, you remembered that you were
using equality properties to solve these
problems!