Question

Help Please!

Janine is considering buying a water filter and a reusable water bottle rather than buying bottled
water. Will doing so save her money?
How much water does Janine drink in a day?
She normally drinks 3 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 $3.99.
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. 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. Refill filters cost about @20 for a 4-pack. the box says each filter last for 40 gallons or 2 months.
an under -sink filter costs $130. refill filters cost $60 each. The filter last for 500 gallons

Answer 1

If a 24 pack of bottles costs $3.99, how much does each bottle cost? From that, find out the cost of 1 ounce of water from purchased bottled water (cost of a bottle / size of bottle).

Find Janine's daily consumption by multiplying 3 bottles/day * size of a bottle.

Find Janine's daily cost for purchased bottled water by multiplying her daily consumption by the cost of 1 ounce of water from purchased bottled water.

A faucet-mounted filter costs $28, plus $33 for a 3-pack of filters. Each filter filters 100 gallons. Assume the water itself is free. Filters are $33/3 = $11 each, so we pay $11/100 gallons, plus an extra $28 one-time cost for the filter attachment. We need to convert gallons to ounces, so we multiply by 128 ounces/1 gallon:

\[\frac{$11}{100 { gal}*\frac{128 oz}{1 gal}} = $11/12800 oz \]

Our cost for x ounces of water (including the bottle and equipment) would be
\[$10 + $28 + \frac{$11}{12800 oz}*x\]

To find the point at which it starts to make more sense for Janine to bottle her own water, set the equation for the cost of x ounces of water = the cost of the volume of bottled water she would drink in the same amount of time. At that point, both costs are equal.

The water filter pitcher case is a bit trickier because the filter needs to be replaced after a certain volume of water or a certain amount of time, whichever comes first. Use the time the filter lasts and the amount of water she consumes per day to find out whether to use the filter's longevity or its capacity to find the cost per volume of water filtered.