Expert: Scott A Wilson - 3/18/2010

Question
I'm 13 years old, in 8th grade. I'm homeschooled (though I'll be going to high school next year).

I just started working on algebra 1. I have a fairly solid understanding of the concepts so far... except for story problems. I just can't seem to figure them out. If it's not an algebra story problem, I can usually solve it, but the algebra ones really just stump me. Unless it's presented like "one plus a number equals 2" or something really obvious like that, I get really confused. :(

Here's an example of story problem I got wrong:

"Mary's mail order business sells books for $3 each plus $5 shipping on any order.

Write an equation that describes the amount spent as a function of the number of books purchased. Then, determine how many books can be purchased for $50."

The answer was 3b + 5 = 50. (b = number of books bought). I didn't understand why I had to multiply the number of books by 3 until my dad explained it to me...

I don't really get why I'm having so much trouble. If someone gives me an equation, I can do it, but constructing one is much more difficult.

Do you have any advice on how to get better at story problems? Also, a link to a site (or something similar) that contains extra problems I can try to solve would be very helpful. I want to go into physics or even quantum physics, but I don't think that will ever happen if I don't get good at stuff like this. It makes me very depressed to think of my difficulties with math whenever I think about physics. Thank you very much.

Answer
The problem states that it is $3 for each book with a $5 constant.
This means it is 3b + 5.

Since it says "for $50", this means that 3b + 5 = 50 and b needs to be found.
A very good source of problems is http://math.uww.edu/~mcfarlat/141/story141.htm

It gives
The following are examples of specific problem types
Mixture Problem
Distance-Rate-Time Problems
Working with Areas
Areas using Quadratic Equation
Filling the Pool
Equations containing Square Roots
A Box Problem
Nickels, Dimes, and Quaters

Clicing on one will show the problem.
As the mouse is dragged across the problem, the place is at is highlgihted and
the results of that section shown.  It would be good to understand what is meant
eac time the mouse is moved before moving it again.  Continue through each problem
from start to end until each step is understood.  Pretty soon it will be in your
head how to solve each step when it is highlighted.

It is also helpful to write down what each phrase means mathematically.

Another way to do them is draw a picture of what is described,
for a picture is worth a thousand words and it would take forever
to write a 1000 words out.

I tried to find someplace free, but had no luck.
However, I did find

http://psycnet.apa.org/index.cfm?fa=buy.optionToBuy&id=1982-22754-001&CFID=70353...

where an algebra study book full of problems can be purchased for only $12.
It is memory applications for story problems.

A good explanton (which I would print out and post on the wall by my desk) is
http://letsplaymath.files.wordpress.com/2008/01/algebra-story-problems.pdf