Simple Equations from Word Problems

Date: 5/23/96 at 17:53:48
From: Anonymous
Subject: Simple Equations

Dear Dr. Math,

I am in grade seven and I'm having a bit of trouble with some problem 
solving questions. The problems are:

1) The Hight Jets played 40 games in one season. They won 10 more then       
they lost, and they tied 2 games. How many games did the Jets win?

2) Jamal has a coin bank with special compartments for quarters, dimes    
and nickles. In how many different ways can Jamal take out 40 cents?

Thanks.
        - Freddy

Date: 5/30/96 at 14:18:25
From: Doctor Darren
Subject: Re: Simple Equations

1) Well, we know that if we add the number of games they won, the 
number that they lost, and the number that they tied (= 2), then we 
will get 40. Furthermore, they lost 10 fewer games than they won.  
Thus, L = W - 10 and L + W + 2 = 40. Plugging the first equation into 
the second, we get 2W - 8 = 40, or W = 24. Thus, L = 14, and T = 2.

2) If Jamal takes out one quarter, then he still needs to take out 15 
cents, which he can do in two ways (1 Dime and 1 Nickel, or 3 
Nickels).  If he takes out no quarters, than he can take out 0,1,2,3, 
or 4 dimes, which will then determine the number of nickels he needs 
to take out (5N + 10D = 40).

Thus, there are 7 ways he can do it.

I hope this helps.

-Doctor Darren,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/