Tuesday, March 11, 2008

Word Problems - Hints and Tips to Solving Them


Word problems are one kind of math question that ALWAYS gives students troubles, probably because making a connection between the math and the 'real world' situation isn't necessarily the easiest thing to do. Despite that, there are a few pointers that you can try to which will hopefully lead you to the correct solution.

The first tip is to MAKE A LIST OF ALL OF THE INFORMATION THAT YOU ARE GIVEN.

Example:

Joe wants to save money to buy a new Playstation 3. It costs $400 to buy from the store. He has a job which pays him $15 per hour, and he works 6 hours per day. However, to get to and from his job, he has to take the bus, which costs him $2 each way, and he buys lunch each day he works for $6. He also owes his dad $500 from when he borrowed it to buy a new stereo. Taking all of these costs into account, how many days will it take Joe to save up enough money to buy his new Playstation? How much more money does Joe need to earn if he wants to buy it in 5 days?

LIST WHAT YOU KNOW:
PS3 cost = $400
Wages = $15 / hr
Work day = 6 hr / day
Bus fare = 2 x $2 / trip
Lunch = $6 / day
Owes Dad = $500

Next, it is important to IDENTIFY WHAT YOU WANT TO FIND OUT. In this case, we want to find out how many days it will take Joe to save enough to buy his Playstation. Specifically, we want to know how long it will take him to save $400.

The next pointer is to try to CLASSIFY WHAT YOU ARE GIVEN INTO GROUPS. In this question, you can classify things into "Things Related to Making Money" and "Expenses."

Money:
Wages = $15 / hr
Work day = 6 hr / day
Expenses:
Bus fare = 2 x $2 / trip
Lunch = $6 / day
Owes Dad = $500
From here, it might start becoming more apparent what need to be done. In this case, you would find out how much money Joe makes in a day, and also how much he spends in a day.
Earnings = $15 / hr x 6 hr / day = $90 / day
Expenses = 2 x ($2 / trip) + $6 / day = $10 / day
Overall = 90 - 10 = $80
So, Joe saves $80 per day.
Now, he owes his Dad $500, and wants to buy his Playstation for $400... totalling $900. At $80/day, Joes can pay off his Dad and then be able to afford his Playstation in:
$900 / ($80/day) = 11.25 days.... = 12 days (since he can't stop working at 11.25 days). :)
Of course, now that you have an answer, make sure that you answer the question completely.... there's still another part!
If Joe wants to make his purchase, after paying back his dad, in 5 days.....
KNOW:
total cost = $900
time = 5 days
NEED:
savings per day = ?
When you separate what you know from what you don't know, it is very helpful in seeing how to get to the answer. In this case, Joe needs $900 / 5 days = $180. Compared to what he makes right now, he needs to save another $100 per day!
So to summarize, they keys to word problems are to:
IDENTIFY WHAT YOU KNOW (classifying into groups helps here),
DECIDE WHAT YOU NEED TO KNOW,
and MAKE SURE YOU READ AND ANSWER THE ENTIRE QUESTION.
Simple rules, but important nonetheless. :)


1 comment:

  1. thanks you so much! this helped a lot!!

    ReplyDelete

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