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The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It shows the dollar amount taken in each day. Day 1 : hamburgers sold were 200 hot dogs sold were 150. Total money taken in $1,450. Day 2: hamburgers sold were 200 hot dogs sold were 250. Total money taken in was $1,750. What is the cost of a hamburger and the cost of a hot dog?

Hamburger:
Hot Dog:

Respuesta :

The hamburgers are $5 and the hot dogs are $3.

Answer:

Hamburger: $5.

Hot dog: $3.

Step by step explanation:

We have been given a table that shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days.

We will form a system of equation from our given information to find the cost of one hamburger and one hot dog.

Let x be price of one hamburger and y be price of one hot dog.

We are told that on first day of fair 200 hamburgers and 150 hot dogs were sold for $1450.

[tex]200x+150y=1450...(1)[/tex]

While on second day of fair 200 hamburgers and 250 hot dogs were sold for $1750.

[tex]200x+250y=1750...(2)[/tex]

Now we will solve our system of equations by substitution method. From 2nd equation we will get,

[tex]200x=1750-250y[/tex]

Now let us substitute this value in 1st equation,

[tex]1750-250y+150y=1450[/tex]

[tex]-250y+150y=1450-1750[/tex]

[tex]-100y=-300[/tex]

[tex]100y=300[/tex]

[tex]y=\frac{300}{100} =3[/tex]

Therefore, cost of one hot dog is $3.

Now let us substitute y=3 in equation 1 to find cost of one hamburger.

[tex]200x+(150\times 3)=1450[/tex]

[tex]200x+450=1450[/tex]

[tex]200x=1450-450[/tex]

[tex]200x=1000[/tex]

[tex]x=\frac{1000}{200} =5[/tex]

Therefore, cost of one hamburger is $5.    

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