Respuesta :
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,
[tex]2p+4[/tex] that is the number of goldfish she bought. Let 'g' represent the number of goldfish. So we have,
[tex]g=2p+4[/tex]
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,
[tex]x= \frac{1}{4} (2p+4)[/tex]
Altogether she has 35 fish, so the sum of all the fishes should be 35,
[tex]p+ (2p+4)+2+\frac{1}{4} (2p+4)=35[/tex]
multiplying both the sides of the equation by 4, we get,
[tex]4p+4(2p+4)+8+(2p+4)=140[/tex]
[tex]4p+8p+16+8+2p+4=140[/tex]
[tex]14p+28=140[/tex]
[tex]14p=140-28[/tex]
[tex]14p=112[/tex]
[tex]p=\frac{112}{14} =8[/tex]
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,
[tex]G= (2 \times 8 + 4)= 16+4=20[/tex]
Hence, Nancy bought 20 goldfish for her aquarium.
Let the number of goldfish be = x
Let the number of platies be = y
As given, she buys goldfish four more than twice the number of platies
So, equation is [tex]x=2y+4[/tex] or [tex]\frac{x-4}{2}=y[/tex]
Number of black mollies = 2
Let the number of guppies be = g
As given, a few guppies that amounted to one quarter of the total number of goldfish she bought.
[tex]g=\frac{x}{4}[/tex]
Now given is that the total number of fish is = 35
So, x+y+2+g=35
So substituting values in terms of x
[tex]x+\frac{x-4}{2}+2+\frac{x}{4}=35[/tex]
[tex]\frac{4x+2x-8+8+x}{4}=35[/tex]
[tex]\frac{7x}{4}=35[/tex]
[tex]7x=140[/tex]
[tex]x=20[/tex]
Hence, the number of goldfish Nancy bought are 20.
If we want to find platies, then y=[tex]\frac{20-4}{2}=8[/tex]
And guppies are 1/4 of 20, so [tex]\frac{1}{4}\times20=5[/tex]
