If 2 sodas and 3 hot dogs are $17 while 5 sodas and 6 hot dogs are $38.75 - how much are each separately?

The cost of soda is $4.75 and the cost of hot dog is $2.5

Step-by-step explanation:

Let us assume :

Given that,

The cost of 2 sodas and 3 hot dogs are $17.

⇒ 2x + 3y = 17  (1)

The cost of 5 sodas and 6 hot dogs are $38.75

⇒ 5x + 6y = 38.75  (2)

Solving the equations to find x and y values :

Multiply eq(1) by 2 and subtract eq(2) from eq(1),

 4x + 6y = 34

-(5x + 6y = 38.75)

 -x         = -4.75

The value of x = 4.75

The cost of soda is $4.75

Substitute x=4.75 in eq(1),

2(4.75) + 3y = 17

3y = 17 - 9.5

3y = 7.5

y = 7.5/3

y = 2.5

The cost of hot dog is $2.5