Questions on Algebra: Proportions answered by real tutors!

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An administrator of a popular web site is told that a new server can handle 41,000 "hits" (users accessing the site) per second. The web site currently experiences a peak demand of about 105,000 hits per second; but every month, the peak demand increases by 2800 hits per second. Use a proportion equation to determine how many new servers the administrator should buy to address expected traffic for the next 24 months.
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[# of servers/hits per sec] = [# of servers/hits per sec]
1/41000 = x/[105,000+24*2800]
x = [105,000+24*2800]/41000
-------
x = 172200/41000
x = 4.2
Rounding up they will need 5 servers to handle the peak demandin 24 mths.
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How many servers do they have NOW?
105000/41000 = 2.56
So, they must have 3 servers NOW.
----------
Ans: they will need 2 new servers in 24 months.
=================================
Cheers,
Stan H.

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A lawyer bills her clients $200 per hour of service. If a client's case requires 39 hours to complete, use proportion to calculate how much the client will owe the lawyer (excluding tax).
------------------------
hrs/charge = hrs/charge
--------------------------
1/200 = 39/x
Cross-multiply to get:
x = 39*200
x = $7800
---
You are totally right.
===============
Cheers,
Stan H.

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A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.
------------------
Use a proportion:
[9 infected/15 sampled] = [x infected/all the PCs]
(9/15) = (x/202)
x = 202(9/15)
x = 202(3/5)
x = 121.2
Round down to get x = 121 infected PC's out of 202
-------------------
Cheers,
Stan H.

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AU | Parsec | Light Year
One AU = | 1 |4.85*10^-6| (1.58)*10^-5 |
One Parsec = |20619| 1 | 3.26 |
One Light Year = |63291| 0.307 | 1 |
.
.307/1=P/1.58*10^-5
P=.307*1.58*10^-5
=4.85*10^-6
.
(1.58)*10^-5 /1=1/A
A=1/1.58*10^-5
=6.33*10^-6
.
A/1=1/4.85*10^-5
=20619
.
L/1=1/.307
=3.26
.
Ed

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7/2=f/e where f and e are the number of fairies and elves respectively
:
2f=7e
:
f=3e+11-----> so lets take f's value and plut it into the first equation
:
2(3e+11)=7e
6e+22=7e
elves
fairies

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6/13=7.8/M
6M=13*7.8
6M=101.4
M=101.4/6
M=16.9 ans.

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and ---> proportion?
>>>Statement of equality, okay.
, cross multiply

, Proportion
Another way,
, divide both num & den by 3
----> A
And, , divide both num & den by 5
-----> B
As you see, , proportion.
Thank you,
Jojo

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proportion
cross multiply
divide by 2
centimeters

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We have the following ratio:

5 cm    x cm
---- = -------
2 km    10 km

Start with the given ratio


Multiply both sides by 10


Multiply


Simplify



So our answer is which means that the map distance is 25 cm

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We have the following ratio:

5 cm    x cm
---- = -------
2 km    10 km

Start with the given ratio


Multiply both sides by 10


Multiply


Simplify



So our answer is which means that the map distance is 25 cm

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( yd/min)(ft/yd)=( ft/min)( in/ft)=( in/min)( min/s)=
:
in/sec

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( km/s )( m/km) =( m/s)( s/min)= m/min

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n+3/5=32/5--->subtract 3/5 from both sides
or 5 and 4/5ths

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you total up the what was spent 28+20+15=63
:
now you divide that by 3 and that gives you an equal amount that each would pay
:
dollars that each person would pay to be equal. Of course
Mary would have to give Tom $6 bucks and Dick would have to give Tom $1 and that would
end with each paying the $21

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Tom, Dick and Mary decided to share expenses for a class party. Tom bought $28
worth of pizza, Dick bought $20 worth of ice cream,and Mary bought $15 worth of
soft drinks. How much should each person pay in order that each of them spends
the same amount of money and how might they accomplish this?
:
How about just adding up the expenses and dividing by 3?
:
Cost per person = = $21
:
Got to thinking perhaps they want to know how much should be exchanged between
them to make sure each pays $21
:
Tom paid $28, so the other two have to pay him
:
Dick gives him 1$, then he's paid $21
Mary give him $6, then she's paid $21
Tom receives $7 so he pays $21

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= amount Fred gets
= amount Grace gets
= amount Aaron gets
Given:
(1)
(2)
(3)
-------------
From (1)
(4)
Now substitute (2) and (4) into (3)
(3)
(4)
Multiply both sides by
(5)
(6)
(7)
Substitute this back in (2)
(2)
(8)
(9)
Substitute (7) into (4)
(4)
{10)
(11)
Fred gets $750, Grace gets $1500, Aaron gets $4500
check:
(1)
(2)
(3)
--------------
(1)
(12)
(13)
--------------
(2)
(14)
(15)
--------------
(3)
(16)
(17)
OK

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Distribute $6,750 among Fred, Grace, and Aaron. Grace should receive twice as much as Fred and Aaron three times as much as Grace.
Fred = x
Grace = 2x
Aaron = 3(2x)
Then:
x + 2x + 3(2x) = 6750
x + 2x + 6x = 6750
9x = 6750
x = 6750/9
x = 750
Fred gets x or $750.
Grace gets 2x or 2(750) = $1,500
Aaron gets 3(2x) or 3(1500) = $4,500
I hope that helps.

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y=.1n
y=.1n/2 ans.

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I believe there are only 2 kinds
:
directly and indirectly
:
y varies directly with x y/x=k
y varies indirectly with x y*x=k
:
:
a third I suppose would be a mixture or combination of those two
:
:
y varies directly with x and indirectly with z (y*z)/x=k

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Start with the given ratio


Multiply both sides by b


Multiply both sides by 5


Multiply 10.5 and 5 to get 52.5


Divide both sides by 7 to isolate "b"


Divide



So our answer is

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(2x+4)/5=30/25
(25)(2x+4)=(5)(30) (good)
50x+29=150 ( 25*4 =100 ) 50x+100=150
50x = 150-100
50x=50
x=1

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did i solve this proportion correctly?
(2x+4)/5=30/25
(25)(2x+4)=(5)(30)
-------------
25*(2x+4) is 50x + 100, not 29. You would have gotten it right, even tho you went the long way around, except for that.
-------------------------
50x+29=150
50x+29-29=150-29
50x=121
(50x)/50=(121)/50
x=2.42
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No.
(2x+4)/5=30/25 = 6/5
2x+4 = 6
2x = 2
x = 1
I don't know why you call it a "proportion", it's an equation.

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The amount of gold jewelry and other products is measured in karats(K), where 24K
represents pure gold, the mark 14k on a chain indicates that the ration between
the mass of the chain is 14:24. If a gold ring is marked 18k and it weighs 0.4
oz, what is the value of the gold in the ring if pure gold in value at $300 per oz?
:
Wouldn't just be:
* .4 * 300 = $90

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A Boeing 747 jet is approximately 230 ft long and has a wingspan of 195 ft. If a scale model of a plane is about 40cm long, what is the model's wingspan?
------------------
Proportion:
x/40 = 195/230
x = 33.91 cm
====================
Cheers,
Stan H.

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Use a proportion to solve. Floral designers often create arrangements where the flower height to container ratio is 5 to 3. The FIU Art Museum wishes to create a floral display for the opening of a new show. They know they want to use an antique Chinese vase from their collection that is 13 inches high. How tall will the entire flower arrangement be if they use this standard ratio?
--------------------
Proportion:
h/13 = 5/3
h = 65/3
h = 21 2/3 inches
=======================
Cheers,
Stan H.

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this question is rather ambiguous. does it have to be even servings?? or can it be partial?? Does the number of people have to be a whole number?? if it has to be even because 3.25/1.25=2.8 then we have to round down to 2 and 2 servings means 6 people served. On the other hand we can use all the ingrediants then we can make 2.8 servings and 2.8*3 = 8.4 people....we will have alot of unused sugar because the low amount of flour limits us. If one had more flour the sugar has the capabilities of making 4.375 servings.

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Condition:

Remember: , EQN 1
Via our Ratio:, cross multiply
--->
, EQN 2----> subst. in EQN 1:

cross multiply
--->
, Number of Anglo Students
via Eqn 1:
, number of Hispanic Students
Check by Ratio in our Condition:
, Close enough, that's what given, unless there's typo.
Thank you,
Jojo

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4:5=4+5=9 elements
986/9=109.555 value of each element
5*109.555=547.778 number of Anglos.
986-547.778=438.222 number of Hispanics.
Proof:
4/5=438.222/547.778
5*438.222=4*547.778
2,191.1=2,191.1

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Every 3 weeks the Story family drinks 24 bottles of juice. At this rate, how many bottles of juice will the family drink in 10 weeks?
-------------------------
24 bottles in 3 weeks is 8 bottles per week.
In 10 weeks, they'll consume 8 x 10, or 80 bottles. If it's hot, maybe even more.

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well, logically if you think this out if car B gets 1/3 the mpg that Car A gets then any gas car A uses would mean that car B would uses 3 times that amount
the way you would write this as a proportion is
27mpg*2gal=9mpg*xgal where x is gal used by car B
54=9x and ......how about that 3 times the amount of car A

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There is a class. The ratio is 5 boys to 4 girls. There are 65 boys. How many girls are there?
.
Let g = number of girls in the class
.
4:5 = g:65
or
4/5 = g/65
g = (4*65)/5
g = 260/5
g = 52 (girls in the class)

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If those 2 visits you had are the basis of the number of fishes in the river, then


, Answer
Thank you,
Jojo

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Find the unit rate. A 12-once bottle of juice costs $1.08. What is the cost per once?
-------------------
Use a proportion:
x/1 = 108/12
x = 9 cents
===============
Cheers,
Stan H.

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1 tank = 16 gallons
70 miles uses up 1/4 tank
full tank will take him 4 times as far = 280 miles.
-----
since a full tank is 16 gallons, and he can go 280 miles, then he gets 280 / 16 gallons = 17.5 miles per gallon.
----
to travel 500 miles at 17.5 miles per gallon, he will use 500 / 17.5 = 28.57142857 gallons of gas.
-----
28.57142857 gallons / 16 gallons tank capacity = 1.785714286 tanks worth of gas.

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485/500 = .97 which is 97% which exceeds their goal by 2%.

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I don't know why you would have to do proprotions to solve this you can just convert it into an equation and simplify.
what is 20% of 125
what means x
is means =
20% means .20
of means times
125 means 125
what is 20% of 125
x = .2(125)
x = 25

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assuming the new server is already taking care of the current demand, then 3 servers must already be in service with a capacity of 3 * 41000 = 123000 hits.
-----
if you are currently experiencing 105000 hits per second, then you have spare capacity of 123000 = 105000 = 18000 hits per second.
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your expected growth in the next 24 months is 24 * 2800 = 67200 hits per second.
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subtract your spare capacity from the expected growth and you have 67200 - 18000 = 49200 growth that you don't have capacity for.
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divide that growth by 41000 and you will need 1.2 additional servers.
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since you can't buy .2 of a server, you will need 2 additional servers.
-----
not sure if this answers your question.
if it doesn't, then resubmit your question to get other answers.
-----

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A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.
-------------
Let "x" be the number of infected PCs.
EQUATION:
x/202 = 9/15
x/202 = 3/5
x = 121 1/5
------------
Rounding down: x= 121
==========================
Cheers,
Stan H.

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F=h/r^2

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You would take 76550 times .53. That would be 40,571.50. That is 53% of 76,550. Hope this helped.

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Let = invt. in stocks
So, = invt. in bonds
Putting into eqn, (assuming money return-interest per year)



---------->
, money invested in stocks
, money invested in bonds
Check,



It make sense to invest in bonds because it has higher interest, right?
Thank you,
Jojo

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If y varies directly as 2x to the power of 3 and y=54 when x =2
Writing what I think it says: It's 2x^3 not (2x)^3
y = k
:
find k when y = 54 and x=2
54 = k
:
54 = 2(8)k
:
54 = 16k
k =
k = 3.375
:
:
Check solution with this k when x = 2
y = 3.375*2*2^3
y = 3.375(2*8)
y = 3.375*16
y = 54

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Well, if it travels 150km in 2 hours, then in 1 hour it will have travelled half as far - ie 75km.
or,mathematically put : speed = distance / time = 150/2 = 75 km/h
So if it does 75km in 1 hour then in 7 hours it will go 7 times as far as that.
distance = 7 X 75 = 525 km.

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