This is a free lesson from our course in Algebra I
When it comes to solving word problems, generally you've to break the problem down
into smaller parts and solve one part at a time. It is necessary to understand that
certain words indicate certain mathematical operations, e.g. "more than", "decreased
by", "times" and "ratio of" mean addition, subtraction, multiplication and division respectively.To be solved, a word problem must be translated into the
language of mathematics, where we use symbols for numbers - known or unknown, and
for mathematical operations. When all is said and done, a word problem, stripped
from inessential details, translates into one or more mathematical equations of
one kind or another. After the equations have been solved, the result can be translated
back into the ordinary language.
(More text below video...)
(Continued from above) To take a specific example, the ratio of 6 more than x to x would mean
(x + 6)/x. A few other things to keep in mind:
= is used for is, are, and equal
< is used for is less/lower than
<= is used for is less than or equal to
> is used for is greater/larger than
>= is greater than or equal to
()2 is used squared
()3 is used for cubed.
E.g. Suzan is ten years older than Bill, and next year she will be twice as old as Bill. How old are they now?
Solution:
convert the above sentence into equations, because equations are what we need to use algebra.
S=10+B S+1=2(B+1)
That is a direct translation of the word problem. Let S represent Suzan's age (this year), and B represents Bill's age.
"Suzan is ten years older than Bill" is an equation
(S=10+B),
but is in words instead of symbols.
"Next year she will be twice as old as Bill" is a little more complicated, but is just another equation
(S+1=2(B+1)).
The translation process seldom gets much more difficult than the above. But, you may have to weed out extra information.
You can get the answer solving the above two equations.
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