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Math 1AX
Math 2AX
Algebra
Study Guide (Notes)
Word Problems
Literal Equations:
Equations with several variables (letters) are called literal equations.
Your job, usually, will be to solve the equation for one of the variables. The
letters that do not represent your desired variable move to the other side of
the equal sign so that the one variable you are solving for stands alone.
Even though there are more letters in these equations, the methods used to
solve these equations are the same as the methods you use to solve all
equations.
Example #1
Steps
Solve for x:
ax + b = c
- b -b
1. Move b
(the opposite of add is subtract)
ax = c - b
2. Move a
(the opposite of multiply is divide)
3. x is what we are solving for and
it stands alone. Done.
Algebraic Representations:
ADD
SUBTRACT
MULTIPLY
add
subtract
multiplied by
sum
difference
of
more than
*less than
product
increased by
decreased by
times
exceeds
diminished by
double
in all
minus
twice
total
fewer
triple
gain
reduced by
plus
* be careful using "less than" - it reverses the order of things
Writing Algebraic Equations:
DIVIDE
divide
quotient
divided equally
per
ratio of
Make sure you write a “let statement” to represent the variable!
1.
Cost for cable TV service in a certain city
is $45 for the installation and $24 a month
Let c = cost, m = months
for service.
c = 24m + 45
Number problem: for 3 months the cost
would be: Cost = $24 • 3 + $45. Replace 3
with m.
2.
If golf balls cost $1.25 and putters cost $79, Let g = golf ball, p = putters
how many of each can the golf team
1.25g + 79p = 150
purchase for $150?
3.
H2O means that water contains two
hydrogen atoms and one oxygen atom.
4.
A cookie recipe calls for twice as many
chocolate chips as walnuts.
5.
Let O = oxygen, H = hydrogen
H = 2O
Let c = chips, w = walnuts
c = 2w
What is the total weight of a filled hot tub,
Let t = total weight, g = gallons
if the tub weighs 350 pounds and the
t = 10g + 350
water weighs 10 pounds per gallon?
Ratio/Proportion/Percent:
A ratio is a comparison of two quantities.
Since a ratio can be written as a fraction, it can also be written in any form
that is equivalent to that fraction. All of the following are equivalent:
A proportion is a comparison of ratios.
Solve for x in this proportion:
A proportion is an equation that
states that two ratios are equal,
such as
Cross Multiply to solve proportions!
1.
You normally work at the mall over the spring break for $450. This year the boss tells
you that you will be receiving a 7% raise. How much of an increase will you be
receiving? How much will you be earning in total this year?
Solution:
Your raise is 7% of your old salary.
Let r = your raise
r = 7% • 450
r = 0.07 • 450 changing 7% to a decimal
r = 31.5
Your raise will be $31.50.
Your total earnings will be $450 + $31.50
which equals $481.50.
Consecutive Integers, Consecutive Odd Integers, Consecutive Even
Integers:
Consecutive Integers are integers that are “in order” and increase by 1.
Ex. 1,2,3 or -3,-2,-1
Consecutive Odd Integers are odd numbers that are “in order and increase
by 2.
Ex. 1,3,5 or -5,-3,-1
Consecutive Even Integers are even numbers that are “in order” and increase
by 2.
Ex. 2,4,6 or -6,-4,-2
To solve a word problem using consecutive integers, you must set up a LET
statement.
Consecutive Integers
Consecutive Odd
Consecutive Even
Let x = First C.I.
Let x = First C.O.I
Let x = First C.E.I
Let x + 1 = Second C. I
Let x + 2 = Second C.O.I Let x + 2 = Second C.E.I
Let x + 2 = Third C. I.
Let x + 4 = Third C.O.I
Let x + 4 = Third C.E.I
And so on….
And so on….
And so on….
Example:
The sum of three consecutive odd integers is 153. Find the integers.
Let x = First C.O.I.
Let x + 2 = Second C.O.I
Let x + 4 = Third C.O.I
x + x + 2 + x + 4 = 153
3x + 6 = 153
3x = 147
x = 49
49
50
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