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 with explanation:

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

Given : 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.

Then we have a system of two linear equations in two variables :_

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

Multiply 2 to the each side of equation (1), we get

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

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

$y=1000$

Substitute the value of y in (1), we get

$x+1000=2600\\\\\Rightarrow\ x=1600$

Hence,  1600 sodas and 1000 hot dogs were sold.