Answer:
16
Step-by-step explanation:
Let's assume that Nancy bought 'p' numbers of platies. The question says, she buys goldfish, 4 more than twice the number of platies.
So, 4 more than twice of 'p' can be written as,
that is the number of goldfish she bought. Let 'g' represent the number of goldfish. So we have,
![g=2p+4](https://tex.z-dn.net/?f=g%3D2p%2B4)
She also buys 2 black mollies and a few guppies that amounted to one quarter of the total number of goldfish she bought. Let 'x' represent the number of guppies, so we have,
![x= \frac{1}{4} (2p+4)](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B1%7D%7B4%7D%20%282p%2B4%29)
Altogether she has 35 fish, so the sum of all the fishes should be 35,
![p+ (2p+4)+2+\frac{1}{4} (2p+4)=35](https://tex.z-dn.net/?f=p%2B%20%282p%2B4%29%2B2%2B%5Cfrac%7B1%7D%7B4%7D%20%282p%2B4%29%3D35)
multiplying both the sides of the equation by 4, we get,
![4p+4(2p+4)+8+(2p+4)=140](https://tex.z-dn.net/?f=4p%2B4%282p%2B4%29%2B8%2B%282p%2B4%29%3D140)
![4p+8p+16+8+2p+4=140](https://tex.z-dn.net/?f=4p%2B8p%2B16%2B8%2B2p%2B4%3D140)
![14p+28=140](https://tex.z-dn.net/?f=14p%2B28%3D140)
![14p=140-28](https://tex.z-dn.net/?f=14p%3D140-28)
![14p=112](https://tex.z-dn.net/?f=14p%3D112)
![p=\frac{112}{14} =8](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B112%7D%7B14%7D%20%3D8)
Hence, Nancy bought 8 platies. Now that we know the number of platies, we can find the number of goldfish that she bought.
We know that she bought (2p+4) number of goldfish, putting the value of 'p', we get,
![G= (2 \times 8 + 4)= 16+4=20](https://tex.z-dn.net/?f=G%3D%20%282%20%5Ctimes%208%20%2B%204%29%3D%2016%2B4%3D20)
Hence, Nancy bought 20 goldfish for her aquarium.