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 for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.

Answer 1

w + s = 4500 and w = s + .25s

Answer 2

The manager has to by 2,000 sodas and 2,500 water drinks.

Explanation:

From the problem we know that the manage needs to buy a total of 4,500 drinks between water and soda, this can be expressed as

`w+s=4500`

Where
`w` is water and
`s` is soda.

Then, it's given that there is needed 25% more water than soda, which can be expressed as

`w=s+0.25s=1.25s`

Which means that water represents 125% of the soda, because we must include the additional 25% more water over soda.

Then, we replace the second relation into the first one

`w+s=4500\\1.25s+s=4500\\2.25s=4500\\s=(4500)/(2.25)=2000`

Now, we replace this value in one equation to obtain the other one

`w+2000=4500\\w=4500-2000\\w=2500`

Therefore, the manager has to by 2,000 sodas and 2,500 water drinks.