Question

THIS QESTION IS IMPOSSIBAL ANYONE WHO CAN ANSWER GETS MEDAL!!!!
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

20 caviar sandwiches, and 0 of all other sandwiches.

Answer 2

nope @OrangeMaster

Answer 3

Tricky.
Set up your equations:
C = # of caviar
B = # bologna
L = # of liverwurst

C + B + L = 100
5C + 2B + L/10 = 100

multiply the 2nd equation by 10 and subtract the two
49C + 19B = 900

Now, there are lots of ways to do that, but you need both C and B to be integers. Notice that 900 is divisible by 10. Divide the whole equation by 10
$4.9 C + $1.9 B = $90

Now, we know she need to make exactly $90 selling just caviar and bologna. Each time she sells a sandwich, she'll have to give a dime in change. To get back to an exact dollar figure, she'll need to sell some multiple of 10 sandwiches. So, make the substitution

C + B = 10 n

Now, solve for C and substitute
49 n - 3 B = 90

Remembering that n and B are both integers, n must be a multiple of 3 (divide that equation by 3 and see). So try, n=3, 6, 9, etc.
For n=3, B = 19
For n=6, B = 68
For n=9, B = 117 (which is impossible.)

If B = 19, then C = 11 and L = 70.
If B = 68, then C = -8 which is impossible.

So, the only possible answer is 11 caviar sandwiches, 19 bologna sandwiches and 70 Liverwurst sandwiches.

Answer 4

What do you mean no?

Answer 5

i just explained the answer its tricky! @OrangeMaster

Answer 6

Yeah, that is an answer, but not the only one.

Answer 7

50 liverwurst, 20 bologna, and 11 caviar.

Answer 8

no A possible answer can be:
18 Caviar Sandiwiches = $90
4 Bologna Sandwiches = $8
20 Liverwurst Sandwiches = $2

This all equals $100. There can be many more solutions to this problem but this is one of them.

Answer 9

So, the only possible answer is 11 caviar sandwiches, 19 bologna sandwiches and 70 Liverwurst sandwiches.

I know there are more than one solutions, but in the long thing you posted, you said there was only one. And technically my answer would have worked too. You never said that at least on of every sandwich has to be used. You just said 100 sandwiches.

Answer 10

So, 20 caviar would work.

Answer 11

very nice!