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

Soda = $4.75

Hotdog = $2.5

Step-by-step explanation:

Let the price for soda be A and that of hotdog be B

2 sodas and three hotdogs are $17.

That's

2A + 3B = 17

Also, 5 sodas and 6 hotdogs are $38.75

That's

5A + 6B = 38.75

We now have two equations

Equation 1: 2A + 3B = 17

Equation 2: 5A + 6B = 38.75

Multiply equation 1 by 5 and equation 2 by 2

We have

5 x 2A + 5 x 3B = 5 x 17

2 x 5A + 2 x 6B = 2 x 38.75

10A + 15B = 85

10A + 12B = 77.5

Subtract equation two from equation one

3B = 7.5

Divide both sides by 3

B = 7.5/3

B = 2.5

Now substitute 2.5 for B in either of the equations to get A.

Using equation 1, we have

2A + 3B = 17

2A + 3 x 2.5 = 17

2A + 7.5 = 17

Subtract 7.5 from both sides

2A + 7.5 - 7.5 = 17 - 7.5

2A = 9.5

Divide both sides by by 2

A = 9.5/2

A = 4.75

Each soda cost $4.75 while each hotdog cost $2.5