Question

Hard question
Tell if u give up!!!!!!!!!!!!!!!!
Owen made 100 sandwiches which
she sold for exactly $100. She sold
caviar sandwiches for $5.00 each, the
bologna sandwiches for $2.00, and
the liverwurst sandwiches for 10 cents.
How many of each type of sandwich
did she make?

Answer 1

you have 2 equations with 3 unknowns ...

Answer 2

yes! it is tricky try and solve it i have solved it and got it correct

Answer 3

a+b+c = k
5a+2b+.1c=k

the intersection of 2 planes is a line, not a point.

Answer 4

so?

Answer 5

so, trolololol

Answer 6

it has a solution!!

Answer 7

It has a lot of solutions.

Answer 8

only 1 sollution i have solved it!!

Answer 9

im sure it has a solution, but is that solution unique?

as is:

a = -33.333... + .6333... c
b = 133.333... -1.6333... c

if for some discrete c, a and b are nonnegative integers, then there may well be some solution

we could also setup a grid to determine all the possible combinations

Answer 10

they are whole numbers integers and ofcourse are positive integers

Answer 11

0 >= -33.333... + .6333... c

33.333...
--------- >= c
6.333...



0 >= 133.333... -1.6333... c

133.333...
---------- >= c
1.6333...

this at least gives us a range for the interval of c

Answer 12

shall i give sollution

Answer 13

of course not

Answer 14

ok!

Answer 15

tell me the sollution by tommorow i have to go!

Answer 16

should be .6333 on the top, mistyped the decimal :)

got it

Answer 17

@amistre64 -- I get the same solution
let c = number of caviar sandwiches
b = number of bologna sandwiches
l = number of liverwurst sandwiches
then we get:\[\begin{align}
c+b+l&=100\tag{1}\\
5c+2b+0.1l&=100\tag{2}\\
\therefore 50c+20b+l&=1000\qquad\text{(2) x 10}\tag{3}\\
\therefore 49c+19b&=900\qquad\text{(3)-(1)}\tag{4}\\
\therefore 19b&=900-49c=19\cdot47+7-49c\\
\therefore 19(47-b)&=49c-7=7(7c-1)
\end{align}\]
Therefore \((7c-1)\) must be a multiple of 19 which leads to:\[c=\frac{19m+1}{7}\qquad\text{for m=0.1,...}\]Also, from (4) we can see that:\[c\le17\]Using this we get the only integer solution which is c=11.

Thus c=11, b=19 and l=70

Answer 18

:)

Answer 19

@asnaseer ur great!!!

Answer 20

thank you :)

Answer 21

Did you use the same method to solve?

Answer 22

yes!

Answer 23

then you are also great! :D

Answer 24

lol! shall i ask one more question answer this one!!!

Answer 25

it is best to ask each question separelty

Answer 26

so better to close this and start a new one

Answer 27

yes that's what i am doing

Answer 28

:)