# Problem solving 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?

1
by martel

2014-09-16T21:51:36+08:00
C = number of caviar
B = number bologna
L = number of liverwurst

1st equation
C + B + L = 100
2nd equation    10 cent  = \$1/10
5C + 2B + L/10 = 100

by elimination,
first divide the 2nd equation by 10 and subtract to 1st equation so that we can eliminate L
then we can get
49C + 19B = 900 ,simplifying divide the equation by 10 to becomes more realistic to the problem
4.9 C + 1.9 B = \$90 (equation 3)
to make exactly dollar by selling  caviar & bologna she'll need to sell some multiple of 10 sandwiches
C + B = 10 n
the possible values of n must be multiple of 3 so lets try n = 3,6,9 and so on
by solving further
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