At a concession​ stand, seven hot dog and two hamburger cost ​$10.50​; two hot dog and seven hamburger cost ​$14.25. Find the cost of one hot dog and the cost of one hamburger.

Answer 1

Problem gives you:

7 Hot Dot + 2 Hamburger = 10.50

This is equivalent to: 49 Hot Dot + 14 Hamburger = 73.50. Note I multiple everything by 7. - this is (1)

Problem also gives you:

2 Hot Dot + 7 Hamburger = 14.25

This is equivalent to: 4 Hot Dot + 14 Hamburger = 28.5. Note I multiple everything by 2. - this is (2)

Subtract side by side (1) and (2), on the left you'll eliminate 14 Hamburger. Only 45 Hot Dog remaining. On the right side, you have 45. So 45 Hot Dog = $45. Each Hot Dog is 1.

Substitute to the first piece of info:

7 Hot Dot + 2 Hamburger = 10.50

<=> 7 + 2 Hamburger =10.50

<=> 2 Hamburger = 3.50

<=> 1 Hamburger = 1.75

So the result is Hot Dog = $1, Hamburger = $1.75. Bravo!