Question

at a concession stand, seven hot dog and four hamburgers cost $19.50; four hot dogs and seven hamburgers cost $21.75. Find the cost hot dog and the cost of one hamburger.

Answer 1

Let x represent the cost of a hot dog and y the cost of a hamburger.

Seven hot dogs and four hamburgers cost $19.50. This means that:

`7x+4y=19.50\text{ --------------\lparen1\rparen}`

Four hot dogs and seven hamburgers cost $21.75. This means that:

`4x+7y=21.75\text{ ----------------------\lparen2\rparen}`

Solving simultaneously, we can make x the subject of the formula in equation (2):

`x=(21.75-7y)/(4)\text{ --------------------\lparen3\rparen}`

Substituting this value into the first equation, we have: