Jeff has $1.35 in nickles and dimes. He has a total of 15 coins. How many of each coin does he have?
1 answer:
For this case we propose a system of equations.
We know that a dime equals 10 cents and a nickel equals 5 cents.
So:
x: Let the variable that represents the number of dimes
y: Let the variable that represents the number of nickels
According to the statement we have:
![x + y = 15\\0.10x + 0.05y = 1.35](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2015%5C%5C0.10x%20%2B%200.05y%20%3D%201.35)
We multiply the first equation by -0.10:
![-0.10x-0.10y = -1.5](https://tex.z-dn.net/?f=-0.10x-0.10y%20%3D%20-1.5)
We have the following equivalent system:
![0.10x + 0.05y = 1.35\\-0.10x-0.10y = -1.5](https://tex.z-dn.net/?f=0.10x%20%2B%200.05y%20%3D%201.35%5C%5C-0.10x-0.10y%20%3D%20-1.5)
We add the equations:
![0.10x-0.10x + 0.05y-0.10y = 1.35-1.5\\-0.05y = -0.15\\y = \frac {-0.15} {- 0.05}\\y = 3](https://tex.z-dn.net/?f=0.10x-0.10x%20%2B%200.05y-0.10y%20%3D%201.35-1.5%5C%5C-0.05y%20%3D%20-0.15%5C%5Cy%20%3D%20%5Cfrac%20%7B-0.15%7D%20%7B-%200.05%7D%5C%5Cy%20%3D%203)
So, Jeff has 3 nickels
![x + y = 15\\x + 3 = 15\\x = 15-3\\x = 12](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2015%5C%5Cx%20%2B%203%20%3D%2015%5C%5Cx%20%3D%2015-3%5C%5Cx%20%3D%2012)
Jeff has 12 dimes.
Answer:
12 dimes and 3 nickels
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