SOLUTION: Mark gets $1.85 a week for an allowance. He always gets 16 coins. the coins are always nickels, dimes, and quarters. How many of each type of coin does he receive?

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Mark gets $1.85 a week for an allowance. He always gets 16 coins. the coins are always nickels, dimes, and quarters. How many of each type of coin does he receive?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 259103: Mark gets $1.85 a week for an allowance. He always gets 16 coins. the coins are always nickels, dimes, and quarters. How many of each type of coin does he receive?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

The system of equations is

system%28n%2Bd%2Bq=16%2C%0D%0A5n%2B10d%2B25q=185%29

Solving that system for n and d in terms of q you get:

system%28n=3q-5%2Cd=21-4q%29

To have a positive number of nickels, we must have at least 
2 quarters.  To have a positive number of dimes, we have to 
have no more than 5 quarters

So if we have 2 quarters, 
then we have n=3(2)-5 or 1 nickel, and d=21-4(2)=13 dimes 

If we have 3 quarters, 
then we have n=3(3)-5 or 4 nickels, and d=21-4(3)=9 dimes

If we have 4 quarters, 
then we have n=3(4)-5 or 7 nickels, and d=21-4(4)=5 dimes

If we have 5 quarters, 
then we have n=3(5)-5 or 10 nickels, and d=21-4(5)=1 dimes

So there are four solutions:

2 quarters, 13 dimes, and 1 nickle
3 quarters, 9 dimes, and 4 nickles
4 quarters, 5 dimes, and 7 nickles
5 quarters, 1 dime, and 10 nickles

Edwin