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Jennifer bought 6 packages of hot dogs and 8 packages of rolls for $41.50. A package of rolls costs $0.85 less than a package of hot dogs. How much did each package of hot dogs cost?

Question

Jennifer bought 6 packages of hot dogs and 8 packages of rolls for 41.50.Apackageofrollscosts41.50. A package of rolls costs 0.85 less than a package of hot dogs. How much did each package of hot dogs cost?

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Solution

Let's denote the cost of a package of hot dogs as x.

According to the problem, a package of rolls costs 0.85lessthanapackageofhotdogs,sowecandenotethecostofapackageofrollsasx−0.85 less than a package of hot dogs, so we can denote the cost of a package of rolls as x - 0.85.

Jennifer bought 6 packages of hot dogs and 8 packages of rolls for a total of $41.50. This gives us the equation:

6x + 8(x - 0.85)=0.85) = 41.50

Solving this equation will give us the cost of a package of hot dogs.

First, distribute the 8 to both terms inside the parentheses:

6x + 8x - 6.80=6.80 = 41.50

Combine like terms:

14x - 6.80=6.80 = 41.50

Add $6.80 to both sides to isolate the term with x:

14x = $48.30

Finally, divide both sides by 14 to solve for x:

x = $48.30 / 14

x = $3.45

So, each package of hot dogs costs $3.45.

This problem has been solved

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