A concession-stand manager buys bottles of water and soda to sell at a football game.

Question

A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations the manager could use to find out how many bottles of water and soda to buy.

= 4500

w =

im so lost

Answer 1

Hi Emily, with the information given, it is not necessary to create a system of equations to solve for the number of bottles of water and soda.

 

In fact, there is not enough information to create a system of equations. Here is an example of what is needed to create a system of equations.

 

A school play sold 100 tickets and earned $300 for their one performance. The adult tickets cost $2.00 and the child ticket cost $1.00. How may adult and child tickets were sold.

 

Now I can say: A (adult tickets) + C (child tickets) = 100

 

And 2A (cost of adult tickets times the number of adults) + 1C (cost of child ticket times the number of children) = 300

 

or:

 

    A + C = 100

  2A + C = 300

 

I can solve this system of equations for A and C.

 

In your example, I have only enough information to create one equation, but that equation is enough to solve the problems.

 

Let S be the number of bottles of sold, then the number of bottles of water will be 1.25 * S. The number of bottles of both is 4500.

 

The equation:

 

S + 1.25S = 4500

 

Solve for S:

 

2.25S = 4500

 

Divide both sides by 2.25:

 

S = 2000, or the number of bottles of soda is 2000.

 

The number of bottles of water is: S + .25S, or 2000 + 500 = 2500.

 

Answer:

 

The number of bottles of water equals 2500 and the number of bottles of soda equals 2000.

 

Questions?