math problem help

Question

Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?

First, determine what information you need to answer this question, then click here to display that info (along with other info).

1. How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.
2. How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.69.
3. How much does a reusable water bottle cost? About $10.
4. How long does a reusable water bottle last? Basically forever (or until you lose it).
5. How much does a water filter cost? How much water will they filter?
6. A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)
7. A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months
8. An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.

Which option is cheapest over one year (365 days)? Select an answer Water bottles faucet-mount filter filter pitcher under-sink filter  

The cheapest option saves her $ over a year.

Give your answer to the nearest cent. Pro-rate the costs of additional filters (so if you only use part of a filter, only count the corresponding fraction of the filter cost) and pro-rate the cost of the bottled water (so if you only use a part of a case, only count the cost for the portion of the case used).

Answer 1

This will just be a lot of figuring. I can help you get started, but you will need to finish the calculations for each option.

First, figure out how much water she drinks per year. That is 16.9 * 4 * 365 = 24,674 ounces per year. This isn't entirely useful since the water filters are in terms of gallons. A gallon is 128 ounces, so we convert:

24,674/128 = 142.76 gallons, which we can round up to 143 gallons (we give the extra to her cat :-).

Knowing how many gallons she drinks per year gives you how many filters you need.

Next, figure out how many water bottles she uses per year, if she buys bottled water. 365 * 4 = 1460 bottles per year. Divide that by 24, the number in each case. 1460/24 = 60.8 rounded up to 61 cases per year because you can't buy .8 of a case.

Now you have some information to start your calculations per option.

1) Bottled water, 61 cases * $3.69 per case =

2) Faucet mounted: $28 + $33 for filters + $10 for the reusable bottle =

3) Pitcher: $22 + $20 for filters + $10 for the bottle =

4) Under sink: $130 + $10 for the bottle =

(the filter probably needs to be changed once per year at her drinking rate, just to keep green things from growing in it... but we're only considering a year so it won't need changing out)

Now, note that this is math.

In real life, she will need more than one reusable bottle because she will go out all day and need two or three.

Also, if she puts the filter on the faucet or under the sink she *will* forget to turn it to "non-filter" for washing dishes probably at least once a week (and her boyfriend will NEVER learn), and she'll start using filtered water to make coffee and oatmeal, so her usage will go up. If that happens, the under-sink filter might be more economical than the faucet filter.

She probably won't use the pitcher accidentally for washing dishes... and it looks like it's the cheapest per year. But the pitchers don't filter out as many contaminants as the faucet or under sink models. Especially if she lives in my town, where we have PFOA contamination. But that's outside the scope of your project. :-)