problem solving

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 3 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 $3.29.
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)?

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

1. The first step in finding how much money Janine will save is to calculate how much water Janine drinks and how much bottled water costs her in one year.
2. To find how much money Janine currently spends on water, calculate the number of cases of water she buys each year (365 days / (24 bottles in a case/ 3 bottle per day) and multiply this number by the price per case ($3.29) to find that Janine currently spends about $150.11 on bottled water every year.
3. To calculate the amount of water Janine drinks each year we multiply the amount she drinks in one day (3 bottles x 16.9oz per bottle) by 365 and then since there are 128 ounces in a gallon, we divide this number by 128 to find that she drinks 144.6 gallons of water each year
4. The next step in this problem is to calculate the cost of each water filter in the first year. To find this, add the cost of the reusable water bottle, the cost of the filter, and the cost of any additional filters needed.
5. The faucet filter costs $28 dollars and includes a filter, plus each additional filter costs $11. Since the filter will last for 100 gallons, we can subtract that amount from the total water she drinks in a year to find the cost of filtering the remainder of the water in the year (144.6 gallons- 100gallons /$11). The total sum of the cost of the faucet filter and reusable water bottle in the first year is $42.91.
6. The pitcher filter costs $22 and each additional filter costs $5. Since the included filter lasts 4 months, Janine will need two additional replacement filters for the other 8 months of the first year. The total sum of the cost for the pitcher filter is $42.
7. The sink filter costs $130 and since the included filter will work for 500 gallons of water, Janine will not need to purchase additional filters in the first year. The total cost of the sink filter is $140.
8. From these calculations, you can see that the pitcher filter is the cheapest option and will save Janine $108.11 in her first year of using this filter.
9. Lastly the question asks you to pro-rate the cost of each filter
10. Since the faucet filters cost $11 each and filter 100 gallons of water, this filter costs 11 cents per gallon and $15.91 per year. She will have to begin replacing these filters approximately 8 months after the initial purchase of the filter.
11. Filtering 40 gallons and costing $5 each the pitcher filter costs 12.5 cents per gallon and $18.08 per year. She will have to replace these filters every 4 months.
12. The sink filter filters 500 gallons of water and costs $60, so it costs 12 cents per gallon and $17.35 per year. She will not have to replace this filter for about 3 and half years after the initial purchase.