Math- Story Problem

Question

Hi, I am really struggling with this question, if anyone could help me solve it, I would appreciate it!!

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.

1. How much water does Janine drink in a day? She normally drinks 4 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 $2.69.
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.

Here is the question that needs to be solved: 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

Hi Annika, I can see why this kind of problem would look very daunting on the surface. It has a lot of information and is asking for a lot of answers. When you encounter a problem like this, it's important to start by asking yourself what the core question they're trying to ask.

How much does it cost Janine to drink water for a full year?

So let's start by looking at what she currently does. She drinks 4 bottles a day, and buys 24 packs for $2.69. That means, every 6 days, she spends $2.69. In a year, that's (365/6)(2.69)=$163.64 per year.

And we'll compare that to each other option. But first, we need to understand how much water Janine drinks, so that we can compare properly with the other options. The amount she drinks is in ounces, and the other options are given in gallons.

We'll use 365/6 to look at how many 24 packs Janine drinks in a year. Then we multiply that by 24 bottles, and 16.9 fluid ounces of water per bottle.

(365/6)(24)(16.9)=24674 fluid ounces of water per year.

Now we convert this to gallons by dividing by 128, giving us 192.77 gallons of water per year.

So we can now look at how much each other option costs her.

If she buys a faucet-mounted filter, she will spend 10 dollars on the bottle, 28 dollars on the filter, and then after 100 gallons have been filtered, she will need another filter. We won't need the whole three pack, we can say that each filter costs $11, and we're going to use 92.77% of it, because after the first filter is used up, Janine will drink another 92.77 out of 100 gallons.

So we set up the equation of 10+28+(11*0.9277)=$48.20

Now we compare with the next option, 10 dollar water bottle, 22 dollar pitcher, and a 4 pack of filters for $20. After the first 40 gallons, we will use the 4 pack of filters to filter 152.77 gallons out of 160 total. Setting up our equation like before, we get:

10+22+(20*(152.77/160))=$51.10

And the last option, 10 dollar water bottle, and we're buying a $130 dollar filter, but we're only using it for 192.77 gallons out of 500. So we set up our equation again...

10+(130*(192.77/500))=$60.12

That means that the faucet mounted filter is the cheapest and will save Janine 163.64-48.20=$115.44 cents per year.

Answer 2

Let's break this down step by step and figure it out together. You're looking to compare the costs of buying bottled water versus using a reusable water bottle and filter over the course of a year. To do this, we need to calculate how much Janine spends on bottled water and then compare it to the cost of the reusable bottle and the cheapest filter option. Here's how we can do it:

1. Calculate the cost of bottled water over a year:

Janine drinks 4 bottles of water a day.

Each bottle is 16.9 ounces, and she buys them in 24-packs for $2.69.

So first, let's find out how many bottles she drinks in a year:

4 bottles per day × 365 days = 1,460 bottles a year.

Next, figure out how many 24-packs she needs:

1,460 bottles ÷ 24 bottles per pack = 60.83 packs per year (we'll round up to 61 packs since you can't buy part of a pack).

Now, multiply the number of packs by the price per pack:

61 packs × $2.69 per pack = $164.09 per year for bottled water.

2. Calculate the cost of the reusable bottle and filters:

Let's consider the cheapest filter option, which is the water filter pitcher:

The pitcher costs $22 initially, and it includes one filter that lasts for 40 gallons.

The refills cost $20 for a 4-pack, and each filter lasts for 40 gallons.

First, determine how much water Janine drinks in a year in gallons:

Janine drinks 1,460 bottles of 16.9 ounces each.

1 bottle = 16.9 ounces, so 1,460 bottles × 16.9 ounces = 24,674 ounces.

Convert ounces to gallons (128 ounces in a gallon): 24,674 ounces ÷ 128 = 192.73 gallons per year.

Now, calculate how many filters she'll need for the pitcher:

Each filter lasts 40 gallons, so 192.73 gallons ÷ 40 gallons per filter = 4.82 filters (we’ll round up to 5 filters).

Now, let's calculate the total cost:

Initial pitcher cost = $22.

She'll need 5 filters total, and the pitcher comes with 1, so she'll need to buy 4 additional filters.

The refill pack is $20 for 4 filters, so she only needs 1 refill pack.

Total cost for the pitcher and filters over the year:

Pitcher: $22.

Refill pack: $20.

Total = $22 + $20 = $42 per year for the pitcher and filters.

3. Compare the costs:

Bottled water: $164.09 per year.

Reusable bottle and water filter pitcher: $42 per year.

4. Calculate the savings:

Savings = Cost of bottled water - Cost of the pitcher and filters.

$164.09 - $42 = $122.09 saved over a year.

So, the cheapest option (the water filter pitcher) saves Janine $122.09 over a year.