Question 270802: A bag of coins contains nickels, dimes, and quarters. There are a total of 17 coins in the bag, and the total amount of money in the bag is $2.00. There is one more dime than there are nickels. How many dimes, nickels, and quarters are in the bag?
Answer by craigt(10)   (Show Source):
You can put this solution on YOUR website! Define the variables:
x = The number of Nickels
y = The number of Dimes
z = The number of Quarters
Define what you know based on the information given as a formula:
1. The total number of coins is 17:
There is one more dime than nickels:
 or 
The total of all coins is $2.
To make this last formula easier to work with, multiply both sides by 100 to
eliminate the decimal places.
So here is our system of equations:
1.
2.
3. 
We were given information to express y in terms of x, so if we can solve for z in terms of x, then we can simply substitute and solve for x.
There are a couple ways to do this. Equations 1 & 2 make it easy to eliminate one of the variables. By adding the two, you can eliminate x and by subtracting 2. from 1. you can eliminate y. By eliminating the x, we would be adding an extra step, so we would like to subtract eq.2 from eq.1 so we can define z in terms of x:
----------------
Solve for z:
We already solved for y:
Now substitute into equation 3.
Simplify:
 or 
Then substitute 6 for x:  , 
Again, substitue 6 for x, now to solve for z:  , 
To check your answers, substitute x, y, and z back into our known formula
,  True
 ,  True
Answer: 6 Nickels, 7 Dimes, & 4 Quarters
|
|
|
