Forgetting Problems on Tests: Is It Normal?

[Tyrion101]

Ok so I remember doing these problems, but for whatever reason when I went to practice this one word problem for the final test I couldn't for the life of me remember how to do it. It's only been two weeks or so since I last worked at it. I remember the other problems fairly well and got this one confused with another, and only figured it out by looking at the tutorial again. Is this normal to forget certain problems here and there, but be reasonably good at remembering the rest?

 

[Mark44]

You might not be approaching the problems in the best way. Usually in word problems, the goal is to translate the relationships in the problem, expressed in English sentences, into one or more equations. Once you have an equation (or equations) that represent the problem, you use algebraic techniques to find the solution. If you are trying to memorize a bunch of techniques rather than one general-purpose technique, that might be causing problems for you.

Can you give us an example of the type of problem that stumped you?

 

[Tyrion101]

The formula for the word problems is c=p-r cost and profit problems, and the formula is also usually something like x-.3x-85=85(.25) and I don't really understand how they get what seems to be an extra 85 in there. I think the reason I forgot these is because I just did it the way the book told me rather than figuring out why the extra number existed. How can you tell when you use a number more than once if it isn't obviously worded that way? Maybe it is and I'm just not seeing the forest through the trees.

 

[Mark44]

The formula for the word problems is c=p-r cost and profit problems, and the formula is also usually something like x-.3x-85=85(.25) and I don't really understand how they get what seems to be an extra 85 in there. I think the reason I forgot these is because I just did it the way the book told me rather than figuring out why the extra number existed. How can you tell when you use a number more than once if it isn't obviously worded that way? Maybe it is and I'm just not seeing the forest through the trees.

This doesn't make any sense: c=p-r

The profit for any sort of business is revenue - costs, or P = R - C.

Revenue is the total money coming in, and costs represent the money being paid out. In simple examples, a company makes one kind of product, which it sells at a certain price, say $10. If it sells x items, the revenue would be R(x) = 10x ($).

Costs come from many things, but in a lot of these simple problems, there are two types of costs: fixed costs that are incurred no matter how many items are produced (mortgage payments, taxes, and so on), and variable costs that depend on how many items are produced (like wages for workers, electricity, and so on).

If the fixed cost is 1000 ($) and the items cost $7 each to make, the cost function would be C(x) = 1000 + 7x ($).

A typical problem is to find the break-even point, the production level at which the profit is 0. That means that the revenue equals the cost, so they set R(x) = C(x), or 10x = 7x + 1000.

Solving this equation, we get 3x = 1000, so x ≈ 333.3 items. If the company sells more than this number, it makes a profit. If it sells fewer than this, it loses money.

 

[Tyrion101]

Well I think I must have had a dyslexic moment, maybe that is why I'm not getting the right answer when looking at it as a word problem :) anyway thank you, I think this makes sense.

 

[Mark44]

Well I think I must have had a dyslexic moment, maybe that is why I'm not getting the right answer when looking at it as a word problem :) anyway thank you, I think this makes sense.

My guess is that you're just trying to blindly apply formulas with little understanding of what they represent. That, and trying to memorize an example from the book, without understanding why the author is tackling the problem that way.

 

[Tyrion101]

Only in this case, I just didn't understand why there was a need to subtract the cost and then multiply it.