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A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 3 bags of potato chips, and 2 soft drinks for $8.50. The price of a hot dog is $0.75 more than the price of a bag of potato chips. The cost of a soft drink is $1.50 less than the price of two hot dogs. Find the cost of each item.

1 Answer

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First we need to understand that the whole problem works around the price of the bag of chips, as the hot dog depends on the price of the bag of chips and the soft drink depends on the hot dog. So analyzing the problem we can say that:

c = bag of chips
h = hot dog
d = soft drink

So we know that hot dog is $0.75 more than the bag of chips, so:

h = c + 0.75

We also know that a soft drink is $1.50 less than 2 hot dogs, so:

d = (2h) - 1.50

As I said the problem will work around bags of chips so we need to know the price of a soft drink in terms of bags of chips, knowing that
h = c + 0.75, we can replace the h in d, so:

d = 2 ( c + 0.75 ) - 1.50

We can simplify this:

d = 2c + 1.50 - 1.50

d = 2c

We know that the total price is 8.50, which is the addition of all the prices of the products (4 hot dogs, 3 bags of chips and 2 soft drinks), so:

So we have

Hot dogs:
4 ( c + 0.75)

Bags of chips:
3c

2 soft drinks:
2 (2c)

With all this we can solve:

4 ( c + 0.75) + 3c + 2 (2c) = 8.50

4c + 3 + 3c + 4c = 8.50

11c + 3 = 8.50

11c = 8.50 - 3

11c = 5.50

c = 5.50 / 11

c = 0.5

So with this we have found the price of a bag of chips, now we just need to replace the value of c in the other variables, so:

Hot dog price:

h = 0.5 + 0.75

h = $1.25

Soft Drink Price:

d = 2(0.5)

d = $1

And with this we have solved the problem, I hope I was helpful.

User Alex Mazzariol
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