The key to working with word problems is to recognize the
meaning of certain words as they relate to mathematical expressions. Then, we
use these symbols in place of the words in the problem, writing an equation. In
particular,
“is” means
“=”
“equals” means “=”
“less” means
“−“
“decrease” means
“−;“
“greater” means “+”
“more” means “+”
“6 is 2 greater than 4” written as:
6 = 2 + 4
“2 is 4 less than 6” written as: 2 = 6 − 4 notice how the 4 and 6
interchange here
“How much more than 12 is 18? written as: “How much” + 12 = 18
What do we add to 12 to get 18? That would be
6. In algebra we replace a phrase like “how much” with a letter, usually x,
then we “solve” for x. We will call “x” the “unknown”. In this case we would
directly write the question as:
x + 12 = 18 we know 6 is
the answer, and we say 6 “solves” this equation, and x = 6.
Example problems:
1)
Three more than a number is 32. What is this number?
3 + x = 32 x must be 29
2)
A number is 12 less than 23. What is this number?
x = 23 − 12 x is 11
3)
Rick started with $5.60. His father gave his loose change to Rick.
Now Rick has $6.72. How much change did Rick’s father give him?
“Gave” in this problem implies
addition. We know what Rick started with; his father added to that amount, the
result is $6.72. From this
We get $5.60 + x = $6.72
subtracting $5.60 from $6.72 we get $1.32 for the answer.
4)
At 10 AM 23 geese were swimming in the pond. Two hours later, only 5
geese were on the pond. How many geese left the pond during these 2 hours?
The number of geese decreased in
this problem; this requires subtraction.
23 − x = 5 To
get 5 from 23 we must subtract 17, so 17 geese left in those 2 hours.
5)
At 5AM a herd of elk were in the park. 60 head walked off leaving 124
head behind. How many head of elk were originally in the park?
Here we know the result, and how
many left, all we need is the starting number. So the starting number minus
the number left is the result.
x − 60 =
124 adding 60 to 124 we get 184 head of elk.
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com