Formulate the situation as a system of two linear equations in two variables. Be

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 $6600 from selling a total of 2800 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?

x = ____________ sodas y =____________ hot dogs

Explanation / Answer

X

= 1800

Sodas

Y

= 1000

Hot dogs

Explanation;

Suppose X sodas were sold and Y hot dogs were sold;

Now let’s put these in the equation;

As per information of the question, total 2800 sodas and hot dogs sold;

X + Y = 2800

Now as per information of the question let’s make second equation;

2X + 3Y = $6600

So let’s solve these equations;

X + Y = 2800………………Equation 1

2X + 3Y = $6600………….Equation 2

Let’s multiply first equation by 3;

3X + 3Y = $8400

2X + 3Y = $6600

On solving these equation;

X = 1800

Now, we can put value of X in equation 1;

1800 + Y = 2800

Y = 1000

Thus, Sodas sold were = 1800

Hot dogs were sold = 1000

X

= 1800

Sodas

Y

= 1000

Hot dogs

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