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 4 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 $3.89.
• 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

Solution:

To save Some amount of money, Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water.

To answer this question, we have to look at the thought process of Janine, that why she has done this?

The information that we need to answer this Question: is Written in Bold Letters

1. Amount of Water Drunk by Janine in a day= 4 × 16.9 Ounces= 67.6 Ounces= Approximately 2 Liter

2. Cost of 24-packs of 16.9 ounce bottles = $3.89

Cost of 4×6 packs of  16.9 ounce bottles =$3.89

Cost of 2 liter or 4 packs of  16.9 ounce bottles =$

3. Cost of Reusable water bottle = $ 10

4. Time for which a reusable water bottle last= Infinitely

5. Cost of a faucet-mounted filter= $ 28

Cost of Refilling for a 3 pack filter=$ 33

So, Cost of Refilling a 1 pack filter= $11

1 filter will filter approximately =100 gallons of water=378 Liters

6. Cost of a water filter pitcher= $ 22

Now, coming to second part ,whether buying a water filter and a reusable water bottle rather than buying bottled water will save her money?

→Total cost of  water filter and a reusable water bottle = $28+$10+ $ (33÷3) ×(Number of times She refills the 3 filter pack)= $ 38 + $11 n

For, 1  water filter and a reusable water bottle total money spent = $ 49

→As the filter contains , 378 Liters of water, and Janine drinks Approx 2 liters of water daily, so 1 filter will last for 189 days.

→1 Liter = 33.81 Ounce

→Cost of 378 liters of water== $ 122.535

So, We can  Surely say that , buying a water filter and a reusable water bottle rather than buying bottled water will save Janine money.

There are 128 oz of water in 1 gallon, so bottled water costs Janine ...

... $3.89/(24×16.9/128) ≈ $1.228 . . . . per gallon

Water filters would cost Janine ...

... $33.00/(3×100) = $0.11 . . . . per gallon

The fixed costs of pitcher and/or faucet-mounted filter are amortized over the number of gallons Janine drinks. After a few hundred gallons, they contribute very little to the overall cost of drinking water.

Janine would save money with water filters after drinking less than 100 gallons.

The amount Janine drinks per day is irrelevant, unless she is on a time schedule to recover her initial costs within some period. The on-going cost is the cost of most interest. The break-even point seems to be on the order of about 3 months, depending on which of the fixed costs Janine chooses to pay.

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )