Word Problem

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).
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 $2.99.
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 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 2 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.

Give your answer to the nearest cent. Pro-rate the costs (so if you only use half of a filter pack, only count half the cost).

Answer 1

1a. Cost per bottle = 2.99/24 (the word "per" means divide so cost per bottle is the same as cost/bottle) 0.1245. Multiply by 6 to get the cost per day.

1b. Or 1 pack of 24 lasts 4 days (24 bottles per pack/ 6 bottles per day.) Cost per day is 2.99/4 * 365

YEARLY COST OF BOTTLED WATER 27.27

2. Re-usable water bottle - they want to know the cost over 365 days.  cost per day (per means divide) cost/day=10/365 = .0273

FIRST YEAR COST FOR REUSABLE WATER BOTTLE $10, EACH SUBSEQUENT YEAR 0

3a. Faucet mount filter cartridge initial purchase cost $28 (comes with one filter) cost per day = 28/365 = .0767

3b. refill cost $33 for 3 (378 liters each.) We can estimate this part to make it easier.

Each water bottle is about 1/2 liter (.4996 liters.)  She drinks 6 bottles a day which is about 3 liters per day and 1,095 liters per year....Each cartridge does 378 liters. 378*4 (number of cartridges with original and 1 refill box) = 1,512. The reason for this logic is she can't buy a partial box. Since we calculated the cost of the first year, for the reusable water bottle, we need to keep that same logic. Therefore first year cost is 28+33=61. The yearly cost will be 1095 (liter drank per year) divided by 378 (liters each cartridge can process) = total number of cartrdiges per year

1095/378 2.89 (can't buy a partial so round-up to 3 cartridges) $33

FIRST YEAR COST FOR FAUCET-MOUNT $61, COST OF EACH SUBSEQUENT YEAR $33

4. Reusable water pitcher. Initial cost $22, $20 for 4 pack, each cartridge does 40 gallons (151.416 liters)

Same thing as above, initial purchase is 5 cartridges which does 151.416*5=757.08 liters.  Ooops, we need 1095 liters. 1095/151.416=7.23, but we have to round-up to 8 because we can't buy a partial cartridge.

First Year = 22 +2*20 (we need two packs) = 22+40=62

After initial year, we will need two packs per year $40

FIRST YEAR COST $62, SUBSEQUENT YEAR COST $40

5. Under sink 130 for first purchase, 60 per filter (500 gallons) 1,892.71 liters. She needs only 1 cartridge per year. In fact, she will only need to buy a cartridge every 1.5 years.

1892.71/1094.124 (number of liters she drinks per year)=1.73 years per cartridge.  We could say that two cartridges last 3 years as an estimate. In this case, the difference is substantial, so lets divide the cost of 2 cartridges by 3 years to see what the yearly cost is. 60*2=120/3=40

FIRST YEAR COST 130, SUBSEQUENT YEARS $40

You will need to re-do the calculations to get the exact change, but this will get you pointed in the right direction.