Word problems (or story problems) usually strike fear into the hearts of young and old math students alike! In all reality, they aren't that bad.
To solve these problems, you look for statements in the problems that describe quantities that are equal. Then, you use algebra to write an equation that can be solved. It is customary to use variables that make it easier to remember what you're looking for, therefore, you don't use x or y in most cases.
1. Problem: The sum of twice a number plus 13 is 75. Find
the number.
Solution:
The word is means equals. The word
and means plus. Therefore, you can
rewrite the problem like the following:
The sum of twice a number and 13 equals 75.
Using numbers and a variable that represents
something, N in this case (for number),
you can write an equation that means the same thing
as the original problem.
2N + 13 = 75
Solve this equation by isolating the variable.
2N + 13 = 75 Equation.
- 13 = -13 Add (-13) to both sides.
-------------
2N = 62
N = 31 Divided both sides by 2.
2. Problem: Find a number which decreased by 18 is 5 times its
opposite.
Solution:
Again, you look for words that describe equal quantities.
Is means equals, and decreased by
means minus. Also, opposite always means
negative. Keeping that information in mind makes it
so an equation can be written that describes
the problem, just like the following:
N - 18 = 5(-N) Equation.
N - 18 = -5N Multiplied out.
5N + 18 5N + 18 Add (5N + 18) to
------------------ both sides.
6N = 18
N = 3 Divide both sides
by 6 to isolate N.