Question

someone please take a look at this...

Answer 1

Three students went shopping for school supplies. Sam paid $6.95 for six notebooks, four pencils, and five pens. Beth paid $2.85 for two notebooks, Five pencils, and three pens, commenting that the "ten cent pen" no longer exists. Assuming that each notebook, each pencil, and each pen cost an exact number of cents, what did Christine pay for one notebook, one pencil, and one pen?

Is the only way to solve this by substitution ? Because I am finding 3 unknown variables and only two equations

Answer 2

I already have these equations...
6n + 4p + 5x = 6.95
2n + 5p + 3x = 2.85

Answer 3

but there is 3 unknown variables

Answer 4

@ganeshie8 ...can you help me

Answer 5

@skullpatrol ....help

Answer 6

it didnt minsion how much Christine paid hmm

Answer 7

am I making this harder then it is ? ....lol

Answer 8

Iknow...it does not say anything about Christine

Answer 9

I can eliminate the n's by multiplying the second equation by -3, but that leaves me with two variables.....do I use substitution for that ?

Answer 10

can this be solved ?

Answer 11

sry i'm blinded
where is this mentioned?
"...it said that Christine payed the same amount for the three items..."

Answer 12

exact number of cents does not mean they cost the same price, does it ?

Answer 13

im not sure abt that
wat i understand from that is
exact number of cent is integer
so
n+p+x=N (such that N is integer)

Answer 14

ugh, wrong again, I should leave, lol, sorry and good luck.

Answer 15

I just thought that meant they cost 10 cents or 25 cents and not .1034....is that right

Answer 16

those are just examples by the way

Answer 17

"ten cent pen" no longer exists.
ill ask this
is there another type of pens ?

Answer 18

I don't know....it does not mention it in the problem.

Answer 19

I wish the pen did cost ten cents, then I could do the problem easily

Answer 20

oh..ic
its confusing me nw
i think ill lev it :o
if its to me ill assume p any number lol

Answer 21

thanks for taking a look and trying to help :)

Answer 22

lol np :P

Answer 23

@TuringTest ..can this be solved

Answer 24

doesn't seem like it has any solutions according to wolfram

Answer 25

I am just gonna skip it and ask my teacher. Thank you for taking a look :)

Answer 26

http://www.wolframalpha.com/input/?i=integer+solutions+6n+%2B+4p+%2B+5x+%3D+695%2C+2n+%2B+5p+%2B+3x+%3D+285%2C+p%3E%3D10

Answer 27

I converted it to cents so we are looking for integer solutions, i.e. only solutions that have an exact number of cents
the way I reason it you can get an equality from the idea that "they no longer make 10c pens"
... oh just realized you used x for pens, let me see if that changes anything

Answer 28

i might have an idea
6n + 4p + 5x = 6.95
2n + 5p + 3x = 2.85
so
n+p+x<=2.85
since
n+p+x=N(such that N is integer)
then
n+p+x=1
or
n+p+x=2

Answer 29

I didn't even realize these could be inequalities...I just thought they were equations

Answer 30

the last statement is a sort of inequality, not the others
it's a "diophantine equation", meaning that there is no formulaic way like substitution to solve it; it is only *possibly* solveable through some unorthodox method like @ikram002p is attempting. I have no idea if that is the right approach, I am terrible with such things :P

Answer 31

this question is really messing with my brain.

Answer 32

looking at it I would simply say "three unknowns, two equations and an inequality, very difficult problem", though again, it may be possible to solve it through some very clever approach, but not something like substitution or elimination or anything straightforward like that.

Answer 33

like I said....I am just gonna ask my teacher. Thank you so much for everything. Thanks to everybody that tried to help :)

Answer 34

welcome, let us know if you get an interesting answer, please

Answer 35

I will do that :)

Answer 36

89 cents, 4 cents and 29 cents respectively.

Answer 37

Another solution: 102, 12, 7

Answer 38

the "no more 10 cent pens" is a bit ambiguous. my first solution assumes that it means there are no pens costing exactly 10 cents. the second solution handles the case where it is meant that there are no pens costing 10 cents or less.