We've already done a lot of word problems, many of which had straightforward translations into mathematical symbols. When word problems contain more words, we naturally need to work a little harder to find good translations. Some may go on for so long that you will wonder why they aren't referred to as "paragraph problems" or "novel problems."
We'll give you some general tips for doing word problems, but first we'll do a short problem to warm up. Then we'll finish with a cool-down on the elliptical.
Ben has twenty-five coins in his pocket, all dimes and nickels. He's going to be disappointed when he discovers that the washing machine only takes quarters. He has half again as many dimes as he has nickels. How much money does Ben have?
First of all:
(number of coins Ben has) = (number of nickels Ben has) + (number of dimes Ben has)
The problem tells us the number of dimes Ben has in terms of the number of nickels he has. Let n be the number of nickels. Then Ben has dimes, since he has half again as many dimes as nickels. Note the difference here: he doesn't have half as many dimes, he has half again as many. Therefore, we'll be taking the amount that is half the number of nickels and adding that to the total number of nickels to find the number of dimes. Make sense? If not, nod your head and smile. We can't take the rejection.
We can now finish translating our first equation into symbols as
Now we have an equation to solve. No more words. Hallelujah. Take a stab at solving the equation and see how you do. See the section on equations if you need a refresher (link).
Hopefully, you got n = 10. If you did, give yourself a pat on the back. If you can't reach it, ask a friend to help you.
The above is all fine and dandy, but "10 nickels'' doesn't answer the question, "How much money does Ben have?'' To find out how much money he has, we add the amount of dough Ben has in nickels and the amount of money he has in dimes. Let's see what ol' Moneybags is worth.
(number of nickels Ben has)(0.05) + (number of dimes Ben has)(0.10)
If Ben has 10 nickels, then he has dimes, so the total amount of money he has is
10(0.05) + 15(0.10) = 2.00.
Excellent. That's almost enough for half a soda from the vending machine.
Now that we're all warmed up, it's time for the promised general tips about what to do with these monsters. The tips come in two flavors:
We used to offer a third flavor, Rum Raisin, but it never got a lot of love so we discontinued it.
Lisa has five times as many books as she has CDs. She must be either over 45 or a librarian. Lisa also has 35 books. Okay, scratch that. She just hates music. How many CDs does she have?