1. There are 100 coins on the table. The coins consist of nickels, dimes, and quarters. The total value is $15.85. How many of each coins are there?
3.
I setup a system of equations.
x = nickels
y = dimes
z = quarters
x + y + z = 100
0.05x + 0.10y + 0.25z = 15.85
I then solve and reduce and get:
x + y + z = 100
y + 5z = 217
I move over variables and get:
x = 100 - y - z
y = 217 - 5z
Since there are more variables than equations I assume that there are many solutions, and try using a parametric representation.
x = 100 - y - z
y = 217 - 5t
where t = any real number
I plug in numbers but end up not getting the value 15.85. The most I can get is somewhere near 14.00.
I was wondering if my setup is wrong.
Is there another way to solve this problem?
3.
I setup a system of equations.
x = nickels
y = dimes
z = quarters
x + y + z = 100
0.05x + 0.10y + 0.25z = 15.85
I then solve and reduce and get:
x + y + z = 100
y + 5z = 217
I move over variables and get:
x = 100 - y - z
y = 217 - 5z
Since there are more variables than equations I assume that there are many solutions, and try using a parametric representation.
x = 100 - y - z
y = 217 - 5t
where t = any real number
I plug in numbers but end up not getting the value 15.85. The most I can get is somewhere near 14.00.
I was wondering if my setup is wrong.
Is there another way to solve this problem?
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