Question

of the box of pens in a box, 2/7 of them are red. of the remaining pens 1/6 of them are blue and the ret are black. there are 280 more black pens than blue pens. how many red pens are there.

Answer 1

The red pens are 168.

Explanation:

Given:

In a box of pens, 2/7 of them are red. of the remaining pens 1/6 of them are blue and the rest are black. there are 280 more black pens than blue pens.

Now, to find the red pens in the box.

Let the total pens be
`x`.

Red pens be
`(2)/(7) of x =(2x)/(7)`

Remaining pens =
`x-(2x)/(7) =(5x)/(7)`

So, blue pens =
`(1)/(6) of (5x)/(7) =(5x)/(42)`

Now, black pens =
`x`-(blue +red)

Black pens =
`x-(2x)/(7)+(5x)/(42)`

According to question:

Black pens = Blue pens + 280

`x-(2x)/(7)+(5x)/(42)`
`=(5x)/(42)+280`

`x-(17x)/(42)=(5x)/(42)+280`

`x-(22x)/(42)=280`

`20(x)/(42)=280`

`x=(280* 42)/(20)`

On solving we get:

`x=588`

So, red pens =
`(2x)/(7)=(2* 588)/(7)`

=
`168`.

Therefore, the red pens are 168.