Question

At a concession, five hot dogs and two hamburgers cost $12.00; two hot dogs and five hamburgers cost $14.25. Find the cost of one hot hot dog and the cost of one hamburger.

Answer 1

Answer : The cost of one hot hot dog and the cost of one hamburger is, $3.75

Step-by-step explanation :

Let the cost of hot dog be, 'x' and hamburger be, 'y'.

Given:

5 hot dogs and 2 hamburgers cost is, $12.00. The equation will be :

`5x+2y=12` ..............(1)

2 hot dogs and 5 hamburgers cost is, $14.25. The equation will be :

`2x+5y=14.25` ..............(2)

Now we have to determine the value of 'x' and 'y' by using substitution method.

`5x+2y=12`

`x=(12-2y)/(5)` ............(3)

Now put equation 3 in 2, we get:

`2x+5y=14.25`

`2((12-2y)/(5))+5y=14.25`

`(24-4y)/(5)+5y=14.25`

`24-4y+25y=71.25`

`21y=47.25`

y = 2.25

Now put the value of 'y' in 3, we get:

`x=(12-2y)/(5)`

`x=(12-2(2.25))/(5)`

`x=(12-4.5)/(5)`

`x=(7.5)/(5)`

x = 1.5

Cost of hot dog = x = $1.5

Cost of hamburger = y = $2.25

Now we have to calculate the cost of one hot hot dog and the cost of one hamburger.

Cost of 1 hot hot dog and 1 hamburger = x + y

Cost of 1 hot hot dog and 1 hamburger = $1.5 + $2.25

Cost of 1 hot hot dog and 1 hamburger = $3.75

Therefore, the cost of one hot hot dog and the cost of one hamburger is, $3.75