Question

A group of friends go out for lunch. If five have hamburgers and four have hot dogs, the bill will be $19.50. If four have hamburgers and five have hot dogs, the bill will be $18.75. What is the price of a hamburger?

A) $3.00
B) $3.50
C) $4.00
D) $4.50

Answer 1

By setting up simultaneous equations based on the given scenarios, we can determine that the price of a hamburger is $2.50, even though this answer does not match the provided choices.

Step-by-step explanation:

To determine the price of a hamburger, let's define the price of a hamburger as H and the price of a hot dog as D. According to the scenarios given, we can set up two equations based on the total cost of the meals:

• 5H + 4D = $19.50
• 4H + 5D = $18.75

We can solve these equations simultaneously to find the values of H and D. Multiplying the first equation by 4 and the second equation by 5 gives us:

• 20H + 16D = $78.00
• 20H + 25D = $93.75

Subtracting the first new equation from the second gives us:

• 9D = $15.75

Dividing by 9 gives us the price of one hot dog:

• D = $1.75

Now we can substitute the value of D into one of the original equations to find H:

• 5H + 4(1.75) = $19.50
• 5H + $7.00 = $19.50
• 5H = $12.50
• H = $2.50

Even though this is not one of the options given in the multiple choices, the answer would be $2.50 per hamburger. However, it’s worth noting that the options provided in the question might be incorrect based on the calculations here.