5. Algebraic Word Problems Flashcards
5 basic types or categories of Algebraic Word Problems
1) Translations (word-for-word translation)
2) Stories: with one or more EQ
3) Age: one or more people (or objects)
4) Value & Quantity: intersection of value and quantity
5) PUQ’s: fractions or % that contain unspecified amounts
Similar in nature, but can have unique wrinkles
add to, sum, plus, more/older/farther/greater than, total, and, increase by, exceed
+
subtract from, difference, minus, less/younger/fewer than, decrease by, lose
-
multiply by, of, by, at, times, product, twice, double, triple, half of, a third of, etc.
x
per, goes into, in, divisible by, out of, for every, quotient, divisor, the ratio of x to y
÷
is, was, has, will be, had, equals, goes for, costs, adds up to, weighs
=
what, a certain number, some number, how many, how much
x, y, etc.
more/older/larger/greater/bigger than
>
less/fewer/younger/smaller than
at least, a minimum, greater than or equal to, no less than
≥
at most, a maximum, less than or greater than, no more than
≤
“Less than” and “greater than” have 2 uses:
1) inequalities
2) addition or subtraction
(typically indicates an amount)
Phrases such as “one thing is less than (or greater than) another” indicate ______
Inequalities
x is less than y
x < y
Richard’s salary is greater than Sarah’s salary
r > s
Alice is younger than Betty
a < b
Phrases such as “one thing is SOME AMOUNT less than (or greater than) another” indicate ________
Addition or subtraction
x is 5 less than y
x = y – 5
Richard’s salary is 1/3 larger than Sarah’s salary
r = s + (⅓ s)
Alice is 4 years younger than Betty
a = b – 4
“One thing is some amount less than another”
be sure to subtract the given amount from the second term!
“x is 3 less than y”
YES
x = y – 3
NO
x – 3 = y
or
x = 3 – y
“There is x times as much of one thing as another’
multiply the second term
“there are three times as many cats as dogs”
YES
c = 3d
NO
3c = d
> > test the relationship with numbers
Any word problem that contains the word “average” should be handled by plugging the provided information into the average formula
Sum of terms
_____________=Average
Number of terms
the word “percent” denotes a number divided by 100 and should be translated as such
Ex:
Q: What number is 15% of 30?
A: x = 15/100 * 30
Translating equally spaced numbers
The sum of four consecutive integers.
x + (x + 1) + (x + 2) + (x + 3)
Translate: The sum of four consecutive odd integers.
x + (x + 2) + (x + 4) + (x + 6)
Translate: Ten is the average of three consecutive even integers.
10 = ( x + (x + 2) + (x + 4) ) / 3
Translate: The sum of three consecutive multiples of 6 is 54.
x + (x + 6) + (x + 12) = 54
4 steps to translate Stories (Alg WP)
1) Read & recognise
_ take time to read
_ locate what problem is after and steps that might get us there
_ diagnosis (particular story problem?)
2) Assign variables & take notes
_ meaningful variables that represent unique quantities
_ take notes
3) Establish Equations
_ look for any sort of stated or implied relationship
4) Solve & double check
Any problem in which a commission, duty tax rate applies only to the
portion of a sale (or income level)
that exceeds a certain limit, must be set up in the following way:
Rate x (Total Value - Limit) = Payment
aka. Rate x (Total - Limit) = Paid
Different types of Alg. WP Stories:
1) Normal
2) Tax, duties, commissions
3) Equation stories
Solving equation stories
Cost, output or value of one activity = that of another
Set the results of the two activities qual to one another
How to solve age problems?
3 steps
Age table
1) browse question and set up an age table
_ how many different people & periods
_ arrange in chronological order
2) Fill out table
_ use one variable only
_ start in NOW column
_ rest of table
3) Find EQ & answer Q
_ find equation
_ check to answer correct Q
How to solve Value & Quantity Mixtures?
Value & Quantity Table (VQT)
1) Set up and fill out VQT
_ Value x Quantity = Total Value
_ one variable (about which the question asks)
2) Find EQ and solve
