Question

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. The concession stand at an ice hockey rink had receipts of $6200 from selling a total of 2600 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold? sodas y = hot dogs x =

Answer 1

Answer: 1000 hot dogs and and 1600 sodas were sold.

Explanation:

Let x be the number of hot dogs and y be the number of sodas.

Given : The concession stand at an ice hockey rink had receipts of $6200 from selling a total of 2600 sodas and hot dogs.

Each soda sold for $2 and each hot dog sold for $3 .

Then, we have the following system of two linear equations:-

`x+y=2600-----------(1)\\\\3x+2y=6200-----------(2)`

Multiplying 2 on both sides of (1), we get

`2x+2y=5200------------(3)`

Now, Eliminate equation (3) from equation (2), we get

`x=1000`

Put x=1000 in (1), we get

`1000+y=2600\\\\\Rightarrow\ y=2600-1000=1600`

Hence, 1000 hot dogs and and 1600 sodas were sold.