The manager at a restaurant keeps track of the number of calzones and slices sold each day and the total money received. on sunday, a total of 59 calzones and slices were sold, and the money collected was $456. if calzones are sold for $9 and slices are sold for $6, how many calzones and slices were sold?

So we set it up like beofre

c=number of calzones
s=number of slices

total of 59 so
c+s=59

total money was 456
9c+6s=456
we can divide both sides by 3 to simplify
3c+2s=152

use subsitution

c+s=59
minus s both sides
c=59-s
subsitute 59-s for c in other equation

3c+2s=152
3(59-s)+2s=152
177-3s+2s=152
177-s=152
minus 177 both sides
-s=-25
s=25

sub back
c=59-s
c=59-25
c=34

34 calzones
25 slices