Final answer:
The cost per package of hot dogs (H) is $5.70, and the cost per package of hot dog buns (B) is $2.40. This was determined by setting up a system of equations from the purchases made and solving for H and B.
Step-by-step explanation:
To solve the problem of determining the cost per package of hot dogs and hot dog buns, we can set up a system of equations based on the information given. We'll let H represent the cost of one package of hot dogs, and B represent the cost of one package of hot dog buns.
From Jonah's first purchase, we have the equation 3H + 2B = 21.90. From his second purchase, we have 2H + 5B = 23.40. Solving this system of equations simultaneously, we can find the values of H and B.
We can multiply the first equation by 2, giving us 6H + 4B = 43.80, and multiply the second equation by 3, yielding 6H + 15B = 70.20. Subtracting the first new equation from the second gives us 11B = 26.40. Dividing both sides by 11 gives us the cost of one package of hot dog buns: B = 2.40. Plugging this value back into the original first equation gives us 3H + 4.80 = 21.90, which simplifies to 3H = 17.10, and further to H = 5.70. Thus, each package of hot dogs costs $5.70, and each package of hot dog buns costs $2.40.