Question

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

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How much water does Janine drink in a day? She normally drinks 6 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 $2.79.
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)?


The cheapest option saves her over a year.

Answer 1

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Answer:

• faucet filter is cheapest
• $205.78 savings first year; $232.78 savings in subsequent years

Explanation:

The variable cost per gallon (128 floz) is ...

water bottles: $2.79/((24×16.9 floz)/(128 floz/gal)) = $0.88 /gal

faucet filter cartridge: $33/(3×100 gal) = $0.11 /gal

filter pitcher: $20/(4×40 gal) = $0.125 /gal

under-sink filter: $60/(500 gal) = $0.12 /gal

a) The cheapest option over the year is the faucet filter.

__

b) The cost of setting up the faucet filter includes the cost of a reusable bottle ($10) and the cost of the faucet mount (less the value of the accompanying cartridge), $28 -11 = $17. The total in addition to the recurring cost is then ...

setup cost = $10 + 17 = $27

and the first-year cost will be ...

$27 + $0.11 g . . . . . where g is the number of gallons used.

The amount of water used in a year (365 days) is ...

(365 days/year)×(6×16.9 oz/day)×(1 gal/(128 oz)) = 289.148 gal/year

Then the cost per year for water bottles is ...

(289.148 gal/year)·($0.8804733 /gal) = $254.59 /year

The cost for the first year for the faucet filter is ...

$27 + ($0.11/gal)(289.148 gal) = $58.81

Janine's first-year savings using a faucet filter will be about ...

$254.59 -58.81 = $205.78

Her savings over subsequent years will be $27 per year more than this.