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?

2 Answers
Oct 5, 2017

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

Oct 5, 2017

$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