Download MATH 0920 Notes

MATH 0930 Notes… Handout
K. Rigdon
3.1 – Changing Application Problems into Equations (pgs 180-193)
This is the beginning of the part of Mathematics that has more to do with understanding
the English language, than it does the understanding of Mathematics…..
Key Words for Addition

Added to…

More than…

Increased by…

The sum of…

Total of…

Older than…
Key Words for Subtraction

Subtracted from…

Less than…

Decreased by…

The difference between…

Reduced by…

Shorter than
Watch the order – subtraction is NOT commutative
Key Words for Multiplication

Multiplied by…

The product of…

Twice…

…times a number…

Of… (when used with fraction or percent)
Also use multiplication when considering…
value of coins,
or calculating sales tax,
or purchasing items at a certain price per item,
or calculating money earned at a certain dollar amount per hour, etc.
Key Words for Division

Divided by…

The quotient of…
Be careful of the order – division is NOT commutative
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 189; #12, 14, 16, 18, 20, 22, 24, 26, 28, 30
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Determining What the Variable Stands For
In a word problem, there will be at least 1 thing that you do not know the value for….
…that is usually what you’re trying to solve for…
…this is what you want your variable to stand for…
…If there are more things that you do not know, there is usually 1 thing that you know the
least about…
…this is what you want your variable to stand for…
…If there is not more information about 1 thing than about another, you get to pick…
Define the Variable – tell what the variable is standing for in your problem
Let x = …….
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 189; #32, 34, 36, 38, 40
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Define the Second Quantity/Other Unknown(s) – if there are other things you do not
know the value for in your problem,…
… you must define them as well,… First define the variable, then…
… using the description from the problem…
… and the SAME variable as you used before…
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 189-191; #46, 48, 54,
58, 60, 62, 64, 66, 70, 72
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
If you don’t know any more about one number than you do about another,
but you know that they ADD UP TO a certain amount…
... pick one to have your variable stand for…
… then use the “total – variable” for the other…
Two numbers that total 13…
Let x = one number
Let 13 – x = other number
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 189-191; #42, 44, 52, 56, 68, 74
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Translating Applications into Expressions with One or more Unknown
1) Define your variable and other unknown(s)
2) Write the expressions showing the relationship with the unknowns
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 191-192; #76, 80, 82, 84,
86, 90, 92, 96, 98
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Translating Applications into Equations
Equations will have equal signs and something on both sides of the equal sign.
……So, your job will be to figure out what to write on each side…..
……then solve the equation you wrote,….so you can answer the question asked in the
problem…… (start this next section)



Key Words for Equal
....is….
….will be….
….was….


….yields….
….gives….
Steps To Set up the Equation from Words
1)
Read the problem
a.
b.
2)
Decide what variable to use & what it will stand for in the problem….. define it…
a.
b.
3)
Pay attention to what kind of problem it is
Pay attention to how many “unknowns” there are
The variable usually stands for what you know the least about in the problem
“Define it” means to write….
x = “something”
If there are more “unknowns”, define them using the description in the problem
and the same variable you used before
2x + 1 = “something”
4)
Look back at the problem to see what you’re supposed to do to the “unknowns”
…if it says…”the sum of their ages is 52”
… “sum” means you are supposed to add
… “is 52” means that will equal 52
x + (2x + 1)
x + (2x + 1) = 52
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 192-193; #100, 104, 106, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
“Consecutive Integers”, “Consecutive Even Integers”, and “Consecutive Odd
Integers”
When you see any of those phrases in a word problem, you know that there is a special
situation and therefore a special was to represent these integers…
Consecutive Integers are numbers that come one right after the other….
Like… 5 and 6…. or -2 & -1…
the secret is that whatever the first one is
the second one is 1 more
so…… the first integer = x
and….. the second integer = x + 1
Consecutive Even Integers are numbers that are both even and come one right
after the other….
Like… 6 and 8…. or -4 & -2…
the secret is that whatever the first one is…
the second one is 2 more (to get to the next even integer)
so…… the first even integer = x
and….. the second even integer = x + 2
Consecutive Odd Integers are numbers that are both odd and come one right
after the other….
Like… 5 and 7…. or -9 & -7…
the secret is that whatever the first one is…
the second one is 2 more (to get to the next odd integer)
so…… the first odd integer = x
and….. the second odd integer = x + 2
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Examples: pg 192-193; #102, 108, 110
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -