Question 622393: a vending machine contains 255 coins which are made up of nickels, dimes and quarters worth $41.25. suppose there are twice as many dimes as nickels, how many of each types are there? can you please help me with this word problem on my homework, word problems are the only thing i do not understand in this class. thank you
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let  represent the number of nickels. Then  represents the number of dimes. Also, let  represent the number of quarters.
The total number of coins, aside from being the number you were given, is the sum of the number of nickels plus the number of dimes plus the number of quarters, so:
The value of nickels, in cents, is  . The value of dimes, in cents, is  . The value of quarters, in cents, is  . The total value of all the coins is given as $41.25. But since the individual values of the types of coins is now expressed in cents, lets express the total value of all the coins as 4125 cents. The sum of the values of the individual types of coins is the total value of all the coins, so:
Simplify each of the equations and then solve the 2X2 system for and and then calculate .
You could have also written the second equation as
But I think integer coefficients are much tidier than decimal fractions, don't you?
John
My calculator said it, I believe it, that settles it
|
|
|
