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,

How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.

How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.79.

How much does a reusable water bottle cost? About $10.

How long does a reusable water bottle last? Basically forever (or until you lose it).

How much does a water filter cost? How much water will they filter?

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)

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

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).

Answer 1

Given that Janine drink 4 bottles a day, each 16.9 ounces.

So, in 1 year (365 days), she drinks = 365*4*16.9 ounces of water

= 24674 ounces of water

= 192.765625 gallons of water

As per given conditions, she have to buy 61 water bottles. But, she have to buy 72 water bottles because of there are 24 bottles in a pack.

So, water bottles cost = $(3.79*3) = $11.37

Given, cost of reusable water bottle = $10

By given conditions, to get 192.765625 gallons, i.e., (100 + 92.765625) gallons of water from faucet-mounted filter, she have to spend = $[28 + (92.765625*33/300 )] = $(28 + 10.2042) = $38.2042 $38.20 (nearest cent)

To get 192.765625 gallons, i.e., (40 + 152.765625) gallons of water from water filter pitcher, she have to spend = $[22 + 152.765625*20/160] = $(22 + 19.0957) $41.0957 $41.10 (nearest cent)

To get 192.765625 gallons of water from under-sink filter, she have to spend = $ 130

The following chart will show how much janine have to spend for 192.765625 gallons of water :

Water bottle packs --------- $11.37

Faucet-mounted filter with reusable water bottle--------- $(10 + 38.20) = $48.20

Water filter pitcher with reusable water bottle ------------$(10 + 41.10) = $51.10

Under-sink filter with reusable water bottle -------------$(10 + 130) = $ 140

So, the cheapest option for her is to buy water bottle packs.

The cheapest option saves her $36.83 (comparing with faucet-mounted filter), $39.73 (comparing with water filter pitcher) and $128.63 (comparing with under-sink filter) over a year.