Answer:
4/9
Step-by-step explanation:
Finally, I can put my answer!
You would find that in the first quadrant.
For this case, the first thing to do is define variables.
We have then:
- <em>x: number of nickels
</em>
- <em>y: number of dimes
</em>
- <em>z: number of quarters
</em>
We write now the system of equations:
![0.05x + 0.1y + 0.25z = 4.10\\y = 2z\\x = y + 5](https://tex.z-dn.net/?f=0.05x%20%2B%200.1y%20%2B%200.25z%20%3D%204.10%5C%5Cy%20%3D%202z%5C%5Cx%20%3D%20y%20%2B%205)
Then rewriting the equations we have:
![0.05 (2z + 5) + 0.1 (2z) + 0.25z = 4.1\\0.05 (2z + 5) + 0.1 (2z) + 0.25z = 4.1\\0.1z + 0.25 + 0.2z + 0.25z = 4.1\\0.55z = 4.1-0.25](https://tex.z-dn.net/?f=0.05%20%282z%20%2B%205%29%20%2B%200.1%20%282z%29%20%2B%200.25z%20%3D%204.1%5C%5C0.05%20%282z%20%2B%205%29%20%2B%200.1%20%282z%29%20%2B%200.25z%20%3D%204.1%5C%5C0.1z%20%2B%200.25%20%2B%200.2z%20%2B%200.25z%20%3D%204.1%5C%5C0.55z%20%3D%204.1-0.25)
![z = \frac {3.85} {0.55}\\z = 7](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%20%7B3.85%7D%20%7B0.55%7D%5C%5Cz%20%3D%207)
Then, substituting values we have:
Finally:
![x = 14 + 5\\x = 19](https://tex.z-dn.net/?f=x%20%3D%2014%20%2B%205%5C%5Cx%20%3D%2019)
Answer:
19 nickels
14 dimes
7 quarters
The constant is 7
The interpretation of this constant is Marcus paying to enter the county fair.