Question

At a concession stand, five hot dog(s) and four hamburger(s) cost $16.75; four hot dog(s) and five hamburger(s) cost $17.00. Find the cost of one hot dog and the cost of one hamburger.

Answer 1

Explanation:

Let x and y denote the cost of one hot dog and the cost of one hamburger.

ATQ,

Five hot dog(s) and four hamburger(s) cost $16.75 and four hot dog(s) and five hamburger(s) cost $17.00

So,

5x+4y = 16.75 ....(1)

4x + 5y = 17 ....(2)

Multiply equation (1) by 4 and equation (2) by 5.

20x+16y = 67 ....(3)

20x+25y= 85 ....(4)

Subtract equation (3) and (4).

20x+16y-(20x+25y) = 67-85

16y-25y = -18

-9y = -18

y = 2

Put the value of y in equation (2).

4x + 10 = 17

4x = 7

x = 1.75

So, the cost of one hot dog is $1.75 and that of cost of one hamburger is $2.