3.4 Expressions and Equations
Goal:
To translate phrases to algebraic
expressions (emphasizing grouping
symbols)
To solve problems by writing and solving
equations
Technique
• Underline key phrases and write
what they mean underneath
• Then put it all together going left
to right
Review of Key Words:
Addition
Subtraction
Multiplication
Division
Review:
Write an expression that means:
5 more than a number “n”
n+5
Review:
Write an expression that means:
9 less than a number “n”
9n
n 9
New Stuff for Translating
Expressions:
•
•
•
•
•
•
Words that means a grouping symbol:
“the sum of”
“the difference of”
“the quantity of”
“the product of”
“the quotient of”
Example 1: 5 times the sum of a
number and 5
5(n + 5)
Example 2:
5 times the quantity 3 less than a number.
5(n – 3)
Remember: with less
than we write the
expression
backwards…
NOT left to right.
Example 3:
14 less than the product of 3 and a #
(3n) - 14
Remember: with less
than we write the
expression
backwards…
NOT left to right.
Example 4:
4 times the quantity 3 greater than a
number
4(n + 3)
Example 5:
One-half the difference of a
number and 1
1
n  1
2
Example 6:
Two fewer than the product of 10 and
a number
10n  2
Translating Equations
•
•
•
•
•
Read the problem a few times
Underline key phrases
Translate from English to Math symbols
Set up your equation
Solve
c
21 = 2
Arthur is two years younger than Chan.
Arthur is 21. How old is Chan?
Example 1:
Let c = the age of Chan.
21 = c - 2
23 = c
Ex 2:
=
The number of salted peanuts in a nut mix
is 13 times the number of cashews. There
are 52 salted peanuts. How many
cashews are there?
Let c = number of cashews
52 = 13 • c
4=c
Ex 3:
Nora divided 315 cans equally among 26
cartons and had 3 cans left over. How
many cans were in each carton?
Let x = cans per carton
(cans per carton)(# cartons) = total cans
+ 3
26x + 3 = 315
Ex 4:
The final exam had three times as many
points as the first test, plus a bonus question
worth 25 points. The final exam was worth
160 points (including the bonus). How many
points was the first test worth?
Let x = points on first test
Final = 3 times first test plus bonus
160 = 3x + 25
Ex 5:
At Max's Restaurant the cost of a child's
dinner is $3.00 less than the cost of an adult
dinner. You bought four children's dinners
and paid $18.00. Find the cost of an adult
dinner. “x”
Child dinner = x - 3
4 • Child dinner = $18
4(x – 3) = 18
Assignment:
Page 133
# 1-16 , 22-26 all
(1-12 write down the
question, 13-16 and 22-26
write down what is most
important from the
question)