Download 5 more than a number “n”

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
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”
“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 and translate the english into
math
 Write down what you know
 Identify what you are trying to find
 Translate into an equation
 Solve
 Check
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:
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