Question

1 file and 1 notebook cost $10. 1 file and 1 pen cost $6. Each notebook costs thrice as much as a pen. How much does 1 file cost?

Answer 1

A files costs `$4`

Explanation:

Let the following variables apply (with all values in dollars):

• `color(blue)f`: cost of a file
• `color(green)n`: cost of notebook
• `color(magenta)p`: cost of a pen

We are told
[1]`color(white)("XXX")color(blue)f+color(green)n=10`
[2]`color(white)("XXX")color(blue)f+color(magenta)p=6`
[3]`color(white)("XXX")color(green)n=3 * color(magenta)p`

From [3] we know we can substitute `3 * color(magenta)p` for `color(green)n` in [1]
[4]`color(white)("XXX")color(blue)f+3color(magenta)p=10`

Subtracting [2] from [4]
[5]`color(white)("XXX")2color(magenta)p=4`
which implies
[6]`color(white)("XXX")color(magenta)p=2`

From [6] we know we can substitute `2` for `color(magenta)p` in [2]
[7]`color(white)("XXX")color(blue)f+2=6`
and, after subtracting `2` from both sides, we get
[8]`color(white)("XXX")color(blue)f=4`

`:.` a file costs `$4`

Answer 2

`$4`

Explanation:

Let the cost of pen be `p`, file be `f` and notebook be `n`.

`f+n=10---A`
`f+p=6---B`
`n=3p---C`
`f=?`

From A & B,
`10 =6+4`
`cancel(f)+n=cancel(f)+p+4`
`n=p+4---D`

Equating C & D,
`3p=p+4`
`3p-p=4`
`2p=4`
`p=2`

From B,
`f+p=6=f+2`
`f=6-2 =$4`