Question

Tracy works at a hot dog stand.

• She sells 3 hot dogs and 2 pretzels for $15.00.
• She sells 5 hot dogs and 1 pretzel for $21.50.
This situation can be modeled by the system of the equations shown below.
3h+2p=15
5h+p=21.5
Then Tracy sells 2 hot dogs and 4 pretzels. What is the total cost of this order?

Answer 1

Answer: the total cost of this order is $14

Explanation:

She sells 3 hot dogs and 2 pretzels for $15.00.

She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is

3h+2p=15 - - - - - - - - - - - -1

5h+p=21.5 - - - - - - - - - - -2

Multiplying equation 1 by 5 and equation 2 by 3, it becomes

15h + 10p = 75

15h + 3p = 64.5

Subtracting, it becomes

7p = 10.5

p = 10.5/7

p = 1.5

Substituting p = 1.5 into equation 1, it becomes

3h + 2 × 1.5 = 15

3h + 3 = 15

3h = 15 - 3 = 12

h = 12/3 = 4

If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be

(4 × 2) + (4 × 1.5)

= 8 + 6 = $14