first of all. I have the answer to my question, I just want an explanation of how to get it

Question

A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot
dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot
dogs and 4 bags of potato chips for $9.25. Find the cost of each item.

i have the answer I just want step by step math to find the solution

thank you 

Answer 1

This question gives a system of equations.  If we let x = price of a hot dog and y = price of a potato chip, then we can convert the sentences into equations.  Think about it, when you buy things, they multiply the price by the number that you buy, then add up all the subtotals.  So 4 hotdogs (4 · x) and 5 bags of chips (5 · y) would add together to be to total price $12. Also, 3 hotdogs (3 · x) and 4 bags of chips (4 · y) add together to be the total price of $9.25.  Here are the equations:

 

(1)  4x + 5y = 12

(2)  3x + 4y = 9.25

 

The best way to solve a system like this is through the elimination method.  We want one of the sets of coefficients to line up in such a way that they cancel when we combine the equations.  If we multiply equation 1 by 3 and equation 2 by -4, then the coefficients on x with become 12 and -12.

 

(3)  12x + 15y = 36

(4) -12x - 16y = -37

 

Adding the equations together reveal a simple equation:

-1y = -1

 

so y = 1  (A bag of chips cost $1)

 

Using the fact that we now know the value of y, we can substitute it back into the original equation 1 and them solve for x.

 

4x + 5(1) = 12

4x + 5 = 12

4x = 7

x = 1.75

 

so a hot dog cost $1.75.