Question

Nancy has a freshwater aquarium at home. She buys goldfish four more than twice the number of platies she bought last Sunday. She also buys 2 black mollies and a few guppies that amounted to one quarter of the total number of goldfish she bought. If there are 35 fish in all, how many goldfish did she buy?

Answer 1

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 $x=2y+4$ or $\frac{x-4}{2}=y$

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.

$g=\frac{x}{4}$

Now given is that the total number of fish is = 35

So, x+y+2+g=35

So substituting values in terms of x

$x+\frac{x-4}{2}+2+\frac{x}{4}=35$

$\frac{4x+2x-8+8+x}{4}=35$

$\frac{7x}{4}=35$

$7x=140$

$x=20$

Hence, the number of goldfish Nancy bought are 20.

If we want to find platies, then y=$\frac{20-4}{2}=8$

And guppies are 1/4 of 20, so $\frac{1}{4}\times20=5$

Answer 2

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,

$2p+4$ that is the number of goldfish she bought. Let 'g' represent the number of goldfish. So we have,

$g=2p+4$

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,

$x= \frac{1}{4} (2p+4)$

Altogether she has 35 fish, so the sum of all the fishes should be 35,

$p+ (2p+4)+2+\frac{1}{4} (2p+4)=35$

multiplying both the sides of the equation by 4, we get,

$4p+4(2p+4)+8+(2p+4)=140$

$4p+8p+16+8+2p+4=140$

$14p+28=140$

$14p=140-28$

$14p=112$

$p=\frac{112}{14} =8$

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,

$G= (2 \times 8 + 4)= 16+4=20$

Hence, Nancy bought 20 goldfish for her aquarium.