Algebra Word problem! Help! please? :)?

Question

Four pencils and six pens cost $2.12. Two pencils and 12 pens cost $3.58. Find the cost of a pencil and the cost of a pen?

Answer 1

Let C be the cost of a pencil and N be the cost of a pen.

4 C + 6 N = 2.12
2 C + 12 N = 3.58

Start with the second equation and multiply both sides by 2...

4 C + 24 N = 7.16
4 C = 7.16 - 24 N

Now substitute for 4 C in the first equation...

4 C + 6 N = 2.12
7.16 - 24 N + 6 N = 2.12
5.04 = 18 N
.28 = N

So pens cost .28 and pencils cost .11

Answer 2

first you take
$2.12 and divide it by 6 (you have 6 pencils)
35 cents

then take
$3.58 and divide by 12 (12 pens)
29 (30) cents

and then one pencil is 35 cents and one pen is 29 cents
so then you have
.35 + .29= ???
and then that is how much 1 pen and 1 pencil costs in CENTS

Answer 3

Let a be a pencil and b be a pen

4a + 6b = 212
2a + 12b = 358

Multiply the first equation by 2 :-

8a + 12b = 424

Take the second equation away :-

8a + 12b = 424 -
2a + 12b = 358
----------------------
6a + 0b = 66

so a = 11

Given that 2a + 12b = 358 and a = 11
we have 22 + 12b = 358 or 12b= 336
therefore b = 28

So a pencil is 11cents, a pen is 28cents

Answer 4

pencils is "x" and pens is "y"

4x + 6y = 2.12
2x + 12y = 3.58

Multiply second equation by negative two so that when I add vertically my x-terms will disappear.

4x + 6y = 2.12
-4x - 24y = -7.16

Adding vertically, I get

-18y = -5.04

Divide both sides by -18

y = 0.28

A pen costs $0.28


Substitute that value into either of your original two equations to find the cost of a pencil.

4x + 6(0.28) = 2.12

4x + 1.68 = 2.12

4x = 0.44

Pencils must cost $0.11 each.

:)

Answer 5

let x = cost of pencil
y = cost of pen
4 x + 6 y = $2.12 . . . . . equation 1
2 x + 12 y = $3.58 . . . . equation 2
x + 6 y = $1.79 . . . . equation 2 divided by 2
. . . . subtract equation 2 from equation 1
3x = $0.33
x = $0.11
6y = $1.79 - $ 0.11 = $1.68
y = $0.28

Answer 6

Pencil = 0.11
PEn = 0.28

Answer 7

Edit:- damn did it wrong sorry