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

16

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= (1)/(4) (2p+4)`

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

`p+ (2p+4)+2+(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=(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 * 8 + 4)= 16+4=20`

Hence, Nancy bought 20 goldfish for her aquarium.

Answer 2

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
`(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=(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+(x-4)/(2)+2+(x)/(4)=35`

`(4x+2x-8+8+x)/(4)=35`

`(7x)/(4)=35`

`7x=140`

`x=20`

Hence, the number of goldfish Nancy bought are 20.

If we want to find platies, then y=
`(20-4)/(2)=8`

And guppies are 1/4 of 20, so
`(1)/(4)*20=5`