Question

The concession stand at a school basketball tournament sells hot dogs, hamburgers, and chicken sandwiches. During one game, the stand sold 16 hot dogs, 14 hamburgers, and 8 chicken sandwiches for a total of $105.00. During a second game, the stand sold 10 hot dogs, 13 hamburgers, and 5 chicken sandwiches for a total of $76.25. During a third game, the stand sold 4 hot dogs, 7 hamburgers, and 7 chicken sandwiches for a total of $56.25. Determine the price of each product. The price of a hot dog is $ . The price of a hamburger is $ . The price of a chicken sandwich is (Type integers or decimals.)

Answer 1

「16 14 8 | 10 13 5 105" 76.25 56.25

where hd is price of each hot dog

hb is price of a hamburger and ch is price of a chicken

augmented matrix

「16 148 105" | 10 135 76.25 1477 56.25

switch R1 and R3

「477 36.25] | 10 13 5 76.25 | 16 148 105

R3=R3-4R1

| 10 135 | 0 -14 -20 56.25 76.25 -120

R2=R2-2.5R1

|0 |0 -4.5 -14 -12.5 -20 | 56.25 -64.375 —120

R3=R3-(14/4.5) R2

47756.25 lo -4.5 -12.5 -64.375 10 0 18.8889 80.27778

gives

ch=4.25

-4.5hd-12.5ch=-64.375

-4.5hd-12.5*4.25=-64.375

hd=2.5

4hd+7*2.5+7*4.25=56.25

4hd+47.25=56.25

4hd=9

hd=2.25

2.25,2.5,4.25