Download Section 1-1 Using Variables SPI 21C: Translate a verbal expression

Section 1-1 Using Variables
SPI 21C: Translate a verbal expression into an algebraic expression or vs.
SPI 22B: Translate a verbal sentence into an algebraic equation or vs.
Objectives:
• Model relationships with variables
• Model relationships with equations, and formulas
Vocabulary
Variables
• A symbol that represents one or more numbers (unknown amount)
• Represented by any letter of the alphabet. EX: a, z, y, h, etc.
Expression
A mathematical phrase that includes numbers, variables, and
operation symbols. EX: n + 7
Equation
A mathematical sentence that uses an equal sign. EX: 3x + 4 = 10
Open Sentence
An equation that contains one or more variables. Ex: 3x + 4 = 10
Common Translation Operations
Determines operation(s) to be performed
+
-
x or () or •
÷ or /
sum
difference
product
divided by
total
fewer than
times
quotient
more than
less than
multiplied
fraction
increased by decreased by twice
The word “Quantity” indicates the use of parenthesis
Write an algebraic expression relating the pay to number of hours
worked.
Hours
Pay (Dollars)
1. What is the pay for 1 hour?
Worked
2. What is the pay for 2 hours?
1
6.50
3. What is the pay for 3 hours?
6.50 x 2
2
4. What is the pay for h hours?
3
6.50 x 3
5. Write an expression to relate pay to
6.50 x h
h
the number of hours worked.
6.50 x h or 6.50h
Write an algebraic expression for each phrase.
a. Seven more than n
n+7
b. The difference of n and 7
n – 7 Begin with 1st value of n
c. The product of 7 and n
7n
n Divide 1st term by 2d term
7
e. Two times a number plus 3 2n + 3
d. The quotient of n and 7
f. 7 less than 3 times a number
3n - 7
Write an algebraic EQUATION that models the problem below.
Music Plus sells all CDs for $10. Write an equation for the
total cost of a given number of CDs.
C = total cost
How many variables do you need to
n = # of CDs bought
define?
Relate by writing the equation:
C = 10n
Write an Equation from a Table of Data
The data in the table represents the number of gallons used
for the number of miles traveled. Write an equation for the
data in the table.
Gallons
Miles
4
6
8
10
80
120
160
200
Relate Miles to number of gallons.
Miles equals 20 times number of gallons
Define variables.
m = miles traveled
g = gallons
Write an expression representing the problem.
m = 20g
For each problem, (a) define a variable and (b) write an expression that
models the problem.
Structure: Sage-N-Scribe
x = number of months; 150 + 475x
x = number of months;
199 + 688(x – 1)
Kagan 2.1.8
n = number of people after the first person
20 + 15n
n = number of games played
10 + .25n