2. P ROBLEM S ITUATION A basketball team stopped at a fast food restaurant after a game. They divided into two groups. One group bought 5 chicken sandwiches and 7 hamburgers for a cost of $24.90. The second group spent $28.80 and bought 5 chicken sandwiches and 9 hamburgers. How much does a hamburger cost?

3. D EFINE V ARIABLES H represents the cost of one hamburger C represents the cost of one chicken sandwich

4. S YSTEM OF E QUATIONS 5C + 7H = 24.90 5C + 9H = 28.80 5C + 7H = 24.90 5C + 9H = 28.80

5. S OLUTION M ETHOD The system of equations is going to solved by the method of elimination. The variable c is going to be eliminated when we subtract the equations.

6. S TEP _1_ OF S OLUTION We eliminate the 5C 5C + 7H = 24.90 5C + 9H = 28.80 ------------------------------- 2H = 3.90

7. S TEP _2_ OF SOLUTION You divide 3.90 by 2 2H = 3.90 H = 3.90 / 2 = 1.95

8. S TEP _3_ OF SOLUTION Use either equation to find C 5C + 7H = 24.90 5C + 7(1.95) = 24.90 5C + 13.65 = 24.90 5C = 11.25 C = 2.25

9. S OLUTION TO THE S YSTEM OF E QUATIONS The solution to the system of equations is (2.25,1.95)

10. C HECK OF S OLUTION 5(2.25)+7(1.95)=24.90 true 5(2.25)+9(1.95)=28.80 true ----------------------------

11. S OLUTION IN THE P ROBLEM S ITUATION Each chicken sandwich is $2.25 and each hamburger is $1.95