A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 4 bags of potato chips, and 5 soft drinks for $15.75.

Question

A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 5 hot dogs, 4 bags of potato chips, and 5 soft drinks for $15.75. The price of a hotdog is $0.75 more than the price of a bag of potato chips. The cost of a soft drink is $1.00 less than the price of two hot dogs. Find the cost of each item.

 

 

 

 

Help! Need work so I can learn how to solve. 

Answer 1

Hi, Mariah. Let x = the number of hot dogs, y = the number of chips, and z = the number of drinks. Then we know:

 

5x + 4y + 5z = 15.75

x = y + 0.75

z = 2x - 1

 

Let's substitute the 3rd equation into the first one. 

 

5x + 4y + 5(2x - 1) = 15.75

5x + 4y+ 10x - 5 = 15.75

15x + 4y = 20.75

 

Now, let's re-write the 2nd equation as x - y = 0.75

 

We now have a system of two equations with two unknowns.

 

15x + 4y = 20.75

x - y = 0.75

 

To solve this, we can multiply the bottom equation by 4 and add.

 

15x + 4y = 20.75

+ 4(x - y = 0.75)

 

19x = 23.75

 or x = 1.25

 

If x = 1.25, then using the one of the equations above, we can solve for y.

x - y = 1.25 - y = 0.75

.50 = y

 

Since z = 2x - 1, then z = 2(1.25) - 1 = 2.5 - 1 = 1.50

 

So, a hot dog is $1.25, chips are 50 cents, and a soft drink is $1.50. Please let me know if you have any questions.