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Algebra Readiness
Chapter 1
Section 3
Lesson 1.3 Use Formulas
Vocabulary and Concepts:
A variable is a letter used to represent
one or more numbers.
A formula gives a relationship between
two or more variables.
Some common formulas are as follows:
Perimeter and Area of a Rectangle
The perimeter p of a rectangle with
length l and width w is :
P=2l + 2w
The area A of a rectangle with length l
and width w is:
A = lw
Perimeter and Area of a Square
The perimeter p of a square with side
length s is:
P =4s
The area A of a square with side
length s is:
A = s²
Distance, Rate, and Time
Distance traveled d is equal to the
speed (rate of travel) r times the
travel time t.
d=rt
Total Cost
The total cost T of n items is the cost
c of one item (the unit cost) times the
number of items.
T=cn
Example 1
Finding Perimeter and Area
International soccer is played on a
rectangular field that has a length of 100
meters and a width of 64 meters. What are the
perimeter and the area of the soccer field?
SOLUTION
P = 2l + 2w
= 2 (100) + 2(64)
Write perimeter formula.
Substitute 100 for l and 64 for w.
= 200 + 128
Multiply.
= 328
Add.
You Try:
A picture frame holds a picture that
has a length of 6 inches and a width
of 4 inches. What are the perimeter
and the area of the picture?
Answer:
What is the length?
6 in.
What is the width?
4 in.
What is the formula for perimeter for this shape?
P= 2l + 2w
P = 2(6) + 2(4)
= 12 + 8 = 20 in.
What is the formula for area for this shape?
A=lw
A=6(4)
= 24 in.²
Example 2: Finding distance
traveled.
A sea turtle travels at an average rate of
about 20 kilometers per day. How far can a
sea turtle travel in 4 days?
d = rt
= 20 · 4
Write the formula for distance
traveled.
Substitute 20 for r and 4 for t.
= 80 km
Multiply.
A sea turtle can travel 80 kilometers in 4 days.
Example 3: Finding total cost.
A school is purchasing 35 microscopes
that cost $119 each for the science
department. What is the total cost?
T = cn
= 119 · 35
= 4165
Write the formula for total
cost.
Substitute 119 for c and 35
for n.
Multiply.
The total cost for 35 microscopes that cost $119 each is
$4165.
You Try:
Kayla bought 26 jars of poster paint.
She paid $3 for each jar. What was
the total cost?
Answer:
What is the formula for finding total cost?
T = cn
What is the cost of one item?
$3
What is the number of items?
26
T = 3 · 26
= $78