|
www.
Increase Brain Power .com |
How To Solve Word Problems
It seems that one of the biggest
challenges many people have in math, is how to solve word problems.
After a recent newsletter I was reminded of this when a reader
emailed me about a riddle in that issue, which was in the form
of a word problem. He had used the "guess and test"
method to arrive at the solution, but was wondering how to solve
problems like this one that were more difficult.
With that in mind, here's the
riddle/word problem, followed by a refresher lesson on algebra
for those of us that have been out of school for a couple decades.
An Example Of A Word
Problem
A pound of onions plus
a pound of carrots costs $2.70 total.
A pound of carrots plus a pound of potatoes costs $2.30 total.
A pound of onions plus a pound of potatoes costs $2.60.
What is the price per pound for each vegetable?
To solve word problems, start
by replacing the statements with symbols, to create a simple
equation. In this case, we can replace the vegetables with the
first letter of each, with each letter representing a pound of
that vegetable. Now the riddle looks something like this:
o + c = $2.70
c + p = $2.30
o + p = $2.60
o = ?
c = ?
p = ?
Now, one method (there are
others) to solve this, is to just combine the first two statements
and make an equation with the last statement on the other side:
o + c + c + p = o +
p + $2.40
We arrived here because we
know that $2.70 plus $2.30 (o + c = $2.70 and c + p = $2.30)
equals $5.00. To make the right side of the equation equal then,
we added $2.40 to the cost of a pound of onions plus a pound
of potatoes, which we know costs $2.60 ($2.60 + $2.40 = $5.00).
If you want to break that down further: $2.60 + x = $5.00, so
we subtract $2.60 from each side and we get x = $2.40.
If you recall your algebra,
you know you can also remove an "o" from each side
and a "p" from each side, and both sides will remain
equal, leaving us with:
c + c = $2.40
or
2 x c = $2.40
To find the value of
c now, just divide each side by 2, and you get:
c = $1.20
Now you can easily
solve for the other costs:
o + $1.20 = $2.70
Subtract $1.20 from
each side and you get :
o = $1.50
And
$1.20 + p = $2.30
Subtract $1.20 from
each side and you get :
p = $1.10
So:
Onions cost $1.50 per
pound.
Carrots cost $1.20 per pound.
Potatoes cost $1.10 per pound.
This may not be exactly how
an algebra teacher would do it, but then I'm not an algebra teacher.
This method works for me, but in any case, it is more important
to understand the principles involved than remember the exact
forms and steps of the algorithms. To solve word problems then,
replace the words with an equation and work out a solution for
each unknown. Then test your solution. Does $1.50 (onions) plus
$1.20 (carrots) equal $2.70? If so, we have a correct solution.
When I was in school, I learned
how to solve word problems more easily than I learned other math,
because word problems at least seemed related to real life. More
abstract math, while used in life by engineers, astronomers and
others, was never presented in such understandable contexts,
and so was more difficult for me. But then, I usually had my
own obscure and difficult to explain algorithms for such problems.
In fact, like the reader who
emailed me, I would have probably used the "guess and test"
method to solve the problem above. Part of using our minds most
efficiently is knowing intuitively when to use one method or
another. Intuition comes into play because it isn't always clear
which way will be quicker, especially with word problems.
Increase Brainpower Home Page | How To
Solve Word Problems |