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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 $2.89.
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

Ok so the first thing you need to figure out is how much Janine is spending on water currently by buying water bottles.

If she drinks 4 bottles each day and there are 24 bottles in a pack at $2.89/pack, she pays $0.48/day for water. Multiplied by 365, she pays $175.81 each year for bottled water.

Now to figure out how much each water filter will cost, you need to know how often Janine will replace her filter. To do that, we need to figure out how many ounces she drinks in a day, then convert that to gallons. Since she drinks 4 bottles that are 16.9oz each, that is 67.6oz/day.

67.6 x 365 = 24,674 oz/year.

There are 128 oz in a gallon: 24,674 / 128 = 192.7 gallons/ year.

Great. Now that we know how much she drinks in a year, we can evaluate each filter system.

For the faucet-mounted system: She will pay $28 for the first 100 gallons but then have to pay $33 for a 3 pack of filters. But she will only have to use one filter, and the price comes out to $0.11/gallon. Bringing her total in one year to $38.20.

For the water filter pitcher: she will pay $22 for the first 40 gallons, but then have to buy a 4 pack of filters for $20. That will bring her to 200 gallons of filtered water at a price of $0.13/gallon, getting her through the first year only paying $41.09.

For the under-sink filter: she will pay $130 for 500 gallons. That will last her over 2 years. Dividing 130 by 500 gives a price of $0.26/ gallon. Multiplied by 192.7, she will pay $50.10 for the year.

Every water filter system is cheaper than buying water bottles, even with a $10 reusable water bottle charge added to each option. However, the cheapest option is faucet-mounted system.