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
