8.2 Describing Relationships and Algebraic Equations
An algebraic equation is a mathematical sentence containing two
expressions separated by an EQUAL SIGN. The expression on the left of
the equal sign has the SAME value as the expression on the right. One or
both of the expressions (each side) MAY contain variables.
Example:
2+5=7
2x + 2 = 4
x – 2 = 3y
You are already familiar with an algebraic equation.
Ex.
A=lxw
Area of a rectangle
Let’s explore another equation.
Customer
Cost ($)
1
4.25
2
8.50
3
12.75
4
17.00
5
21.25
The above chart shows a relationship between the number of riders on
a tour bus (customers) and the cost of providing lunches.
Question: If the tour bus operator spent $89.25 on lunches, how many
customers were on the tour?
What algebraic equation can we make to answer this question?
Answer:
How can I describe a relationship using an algebraic equation?
1. Build the following pattern of squares.
2. Complete the table. In the last row,
write an algebraic expression that
gives the perimeter of a square
having a side length of n toothpicks.
3. Use the expression to copy and
complete an equation that relates to
perimeter, P, to the side length, n.
P=
Side Length Perimeter
(Number of (number of
toothpicks)
toothpicks)
1
1
2
3
4
5
n
4. Use the equation to find the perimeter of a square having a side
length of 9 toothpicks.
5. A square has a perimeter of 40 toothpicks. What is its side length?
Explain how you know.
6. Add toothpicks to create the next squares in this pattern.
7. Complete the table. In the last row,
write an algebraic expression that
gives the area of a square
having a side length of n toothpicks.
8. Use the expression to copy and
complete an equation that relates to
Area, A, to the side length, n.
A=
Side Length Area
(Number of (number of
toothpicks)
squares)
1
4
2
3
4
5
n
9. Use the equation to find the area of a square having a side length of 8
toothpicks.
10. A square has a perimeter of 144 square units. What is its side length?
Explain how you know.
Example 1: Describe a Relationship Using an Equation
To enter an amusement park, you must pay an entrance fee of $20 plus
$3 for each ride ticket.
a) Create a table of values that shows the cost versus the number of
ride tickets purchased.
b) Write an equation to describe the relationship.
c) Find the cost if 8 ride tickets are purchased.
d) Andre has $65 to spend at the amusement park. What is the
maximum number of ride tickets he can purchase?
SHOW YOUR WORK HERE as I do it on the overhead or the board.
a)
Number of Tickets, t
Calculation
Cost, C ($)
b) Examine the pattern. Extend it to find the total cost for t ride tickets
0
1
2
3
20
t
The equation related to cost, C, and the number of ride tickets, t, is:
C=
c) To find the cost if 8 ride tickets are purchased, find C when t = 8.
Method 1: Use the equation you have come up with.
Method 2: Use a graph
Graph the relationship between the cost
and number of tickets. Extend the graph
to find the cost when 8 tickets are purchased.
Use a table of values to help you
Number of
Tickets, t
0
1
2
3
Cost, C ($)
20
d) Determine the value of t when C = 65
Method 1: Work Backwords.
Method 2: Use the graph
from above by extending the
dotted line.
HOMEWORK: Page 350 #1, 2,
Page 351 #3, 4, 5, 6, 7, 8
Page 352 #9, 10, 11