Divide to find the unit rate
2550/30 = ?
2550/30 = 85
Answer: 85 gallons per day
Answer:
We conclude that:
![c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2](https://tex.z-dn.net/?f=c%3D-%5Cfrac%7B5n%7D%7B3%5Cleft%28-n%2B2%5Cright%29%7D%3B%5Cquad%20%5C%3An%5Cne%20%5C%3A2)
Step-by-step explanation:
Given the expression
![\frac{4}{2n}+\frac{5}{3c}=1](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B2n%7D%2B%5Cfrac%7B5%7D%7B3c%7D%3D1)
<u>Let us solve for 'c'</u>
![\frac{4}{2n}+\frac{5}{3c}=1](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B2n%7D%2B%5Cfrac%7B5%7D%7B3c%7D%3D1)
Least Common Multiplier of 2n, 3c: 6nc
Now multiply both sides by LCM = 6nc
![\frac{4}{2n}\cdot \:6nc+\frac{5}{3c}\cdot \:6nc=1\cdot \:6nc](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B2n%7D%5Ccdot%20%5C%3A6nc%2B%5Cfrac%7B5%7D%7B3c%7D%5Ccdot%20%5C%3A6nc%3D1%5Ccdot%20%5C%3A6nc)
Simplify
![12c+10n=6nc](https://tex.z-dn.net/?f=12c%2B10n%3D6nc)
Subtract 10n from both sides
![12c+10n-10n=6nc-10n](https://tex.z-dn.net/?f=12c%2B10n-10n%3D6nc-10n)
Simplify
![12c=6nc-10n](https://tex.z-dn.net/?f=12c%3D6nc-10n)
Subtract 6nc from both sides
![12c-6nc=6nc-10n-6nc](https://tex.z-dn.net/?f=12c-6nc%3D6nc-10n-6nc)
Simplify
![12c-6nc=-10n](https://tex.z-dn.net/?f=12c-6nc%3D-10n)
Factor 12c - 6nc = 6c(2-n)
![6c\left(2-n\right)=-10n](https://tex.z-dn.net/?f=6c%5Cleft%282-n%5Cright%29%3D-10n)
Divide both sides by 6(2-n); n≠2
![\frac{6c\left(2-n\right)}{6\left(2-n\right)}=\frac{-10n}{6\left(2-n\right)};\quad \:n\ne \:2](https://tex.z-dn.net/?f=%5Cfrac%7B6c%5Cleft%282-n%5Cright%29%7D%7B6%5Cleft%282-n%5Cright%29%7D%3D%5Cfrac%7B-10n%7D%7B6%5Cleft%282-n%5Cright%29%7D%3B%5Cquad%20%5C%3An%5Cne%20%5C%3A2)
simplify
![c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2](https://tex.z-dn.net/?f=c%3D-%5Cfrac%7B5n%7D%7B3%5Cleft%28-n%2B2%5Cright%29%7D%3B%5Cquad%20%5C%3An%5Cne%20%5C%3A2)
Therefore, we conclude that:
![c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2](https://tex.z-dn.net/?f=c%3D-%5Cfrac%7B5n%7D%7B3%5Cleft%28-n%2B2%5Cright%29%7D%3B%5Cquad%20%5C%3An%5Cne%20%5C%3A2)
Answer: D
Step-by-step explanation: i did the quiz on it and it was D