Question

You are buying food for a birthday party. You purchase 7 packs of hotdogs and 4 trays of cupcakes for$60. After you buy the supplies, more people RSVP, so you need to buy an additional 2 trays of cupcakesand 1 more pack of hotdogs that cost $15. Determine the systems of equations that models this scenarioPls help thanks

Answer 1

The system of equations that then represents this scenario is

7x + 4y = 60

2x + y = 15

On solving this, we obtain

x = 0, y = 15

Cost of a pack of hotdogs = $0

Cost of a pack of cupcakes = $15

Step-by-step explanation

Let the cost of a pack of hotdogs be x

Let the cost of a tray of cupcakes be y

7 packs of hotdogs and 4 trays of cupcakes cost $60.

7x + 4y = 60

2 trays of cupcakes and 1 more pack of hotdogs cost $15.

2x + y = 15

The system of equations that then represents this scenario is

7x + 4y = 60

2x + y = 15

We can then go ahead to solve this

(7x + 4y = 60) × 1

(2x + y = 15) × 4

7x + 4y = 60

8x + 4y = 60

Subtract equation 2 from equation 1

8x - 7x + 4y - 4y = 60 - 60

x = 0

We can then solve for y

2x + y = 15

2(0) + y = 15

0 + y = 15

y = 15

Hope this Helps!!!