substitution/elimination

Question

During one lunch hour, the school cafeteria sells 8 tuna sandwiches and 5 chicken sandwiches for $49.25. The next day they sell 4 tuna and 7 chicken sandwiches for $43.75. How much do they sell each sandwich for? (please solve using substitution or elimination)

Answer 1

8t + 5c= 49.25

4t+ 7c = 43.75

double 2nd equation, then subtract the 1st equation to eliminate one variable

8t +14c = 2(43.75)

8t + 5c = 49.25

9c = 87.50- 49.25 = 38.25

c = 38.25/9 = $4.25 for chicken

t = (43.75-7c) = (43.75- 29.75)/4= 14/4=$3.50 for tuna

check the answers:

4t +7c

=4(3.5)+7(4.25)

= 14+29.75

= 43.75

8t+5c

=8(3.5) +5(4.25)

=28+21.25

=49.25