Question

Solve the following system word problem.

25.
Sam and Tim ordered food for their colleagues at a local restaurant. Sam ordered 3 personal
pan pizzas and 6 burgers for a total of $43.41. Tim ordered 2 personal pan pizzas and 7
burgers for a total of $40.91.
The cost of each pizza was. And the cost of each burger was

Answer 1

Let p be the cost of a pizza, and b the cost of a burger.
3p + 6b = 43.41
2p + 7b = 40.91
Take twice the first and subtract from three times the second.
9b = 35.91
b = 3.99
Substitute b back in either equation, to get p = 6.49.

Answer 2

burger =$3.99

pan pizza =$6.49

Explanation:

3p+6b=43.41⇒eqn 1

2p+7b=40.91⇒eqn 2

eqn 1 * 2

6p+12b=86.82⇒eqn 3

eqn 2 * 3

6p+21b=122.73⇒eqn 4

eqn 4- eqn 3

9b=35.91

b=3.99

sub b=3.99 in eqn 1

3p=43.41-23.94

p=19.47/3

p=6.49