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Tutors Answer Your Questions about Percentage-and-ratio-word-problems (FREE)
Question 572411: If something goes from 90 bucks to 130, what percentage of an increase is it!
I think I devide 90 by 130 but that comes to .69% or 69% - that seems too high?
Answer by Alan3354(21608)   (Show Source):
You can put this solution on YOUR website!If something goes from 90 bucks to 130, what percentage of an increase is it!
-----------
The increase is 40.
40/90 = 0.4444....
=~ 44% increase
Question 572033: Solve the problem by stating the equation you would use to solve and then solving it. Be sure to show all of your work.
Midtown Antiques collects 6% sales tax on all sales. If total sales including tax are $2300.14, find the portion that is sales tax. Round to the nearest cent.
Linda
Answer by ankor@dixie-net.com(12704)  (Show Source):
You can put this solution on YOUR website!Midtown Antiques collects 6% sales tax on all sales.
If total sales including tax are $2300.14,
find the portion that is sales tax. Round to the nearest cent.
:
Find the amt of the sales (s) without the sale's tax
1.06s = 2300.14
s = 
s = 2169.94
therefore
2300.14 - 2169.94 = $130.20 amt of sales tax
Or
2169.94 * .06 = $130.20
Question 572340: a dealer sold 200 tennis racquets. Some were sold at $18 each and the rest were sold at $33 each. The total reciepts from these sales were $4800. How many $18 racquets did he sell?
I can get the average of $24, but am drawing a blank on the actual formula to use.
Answer by scott8148(5895)  (Show Source):
Question 571902: 3x - 9y = 45
-4x +12y = 20
incosistent or consistent
Answer by Maths68(1166)  (Show Source):
Question 571557: In three minutes a conveyor belt moves 800 pounds of recyclable aluminum from a delivery truck to a storage area. A smaller belt can move the same amount of cans the same distance in 9 minutes. If both belts are being used, how long will it take to move the cans to the storage area.
3/800=9/800 ??
Answer by Alan3354(21608) (Show Source):
You can put this solution on YOUR website!In three minutes a conveyor belt moves 800 pounds of recyclable aluminum from a delivery truck to a storage area. A smaller belt can move the same amount of cans the same distance in 9 minutes. If both belts are being used, how long will it take to move the cans to the storage area.
-----------
The faster belt moves 800/3 pounds/min
The slower moves 800/9 pounds/min
-----
Add them, get the total pounds/min
Invert to get mins/pound
Multiply by 800
--------------------
800/3 + 800/9 = 2400/9 + 800/9 = 3200/9 pounds/minute
--> 9/3200 minutes/pound
*800 pounds = 7200/3200 minutes
= 9/4 minutes
Question 571178: After finding the average of 35 scores, a student carelessly included the average with the 35 scores and found the average of these 36 numbers. The ratio of the second average to the true average was
(A) 1 : 1 (B) 35 : 36 (C) 36 : 35 (D) 2 : 1 (E) None of these
Answer by Theo(2978)  (Show Source):
You can put this solution on YOUR website!i believe the answer is 1:1 which would be selection A.
there's a couple of ways you can prove this.
the first way is to take any average number and any number of data points that make up that average.
assume you have 556 data points whose average is equal to 375.
these numbers were chosen at random.
if we let x equal the total of the numbers, then we get:
x / 556 = 375
if we multiply both sides of this equation by 556, then we get:
x = 375 * 556 = 208500
we have a total of 208500 for 556 data points whose average is 375.
we add the average to this set of data points to get a new total of 208500 + 375.
this is equal to 208875/
we divide this by 557 data points (556 of the original plus the additional data point of the average) to get:
208875 / 557 = 375
this is the exact same average that we original got which makes the ratio of the second average to the true average equal to 1:1.
we can also prove this by formula as follows:
the original average is equal to T/N
T is the total of the data points and N is the number of data points.
the second average is equal to T plus the original average divided by N+1
we know that N is equal to 35 which makes N+1 equal to 37.
our original average becomes T/35
our second average becomes (T + the original average)/37
since the original average is equal to T/35, the second average becomes:
(T + T/35)/36
we can simplify this expression to get:
(36T/35)/36
this is because T is equivalent to 35T/35 which, when added to T/35, becomes 36T/35.
our second average is therefore equal to (36T/35)/36
this is the same as 36T/35 * 1/36 which is the same as 36T/(35*36)
since the 36 in the numerator cancels out the 36 in the denominator, we are left with:
second average = T/35.
this is the same as the original average, so the ratio is 1:1.
Question 571116: The resistance (in ohms) of a circular conductor varies directly with the length of the conductor and inversely with the square of the radius of the conduction. If 50ft of wire with a radius of 6 x 10^-3 inch has a resistance of 10ohms, what would be the resistance of 100ft of the same wire if the radius is increased to 7 x 10^13 inch?
Answer by lwsshak3(2927) (Show Source):
You can put this solution on YOUR website!he resistance (in ohms) of a circular conductor varies directly with the length of the conductor and inversely with the square of the radius of the conduction. If 50ft of wire with a radius of 6 x 10^-3 inch has a resistance of 10ohms, what would be the resistance of 100ft of the same wire if the radius is increased to 7 x 10^13 inch?
**
Resistance=10(100/50)[(6*10^-3)/(7*10^13)]^2
=20(6*10^-16)/7)=(120/7)*10^-16≈17.14*10^-16 ohms
Question 570803: 20% of 30 professional r mathematician how many mathematician it should hire so the ratio vll become 10/11
Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!20% of 30 professional r mathematician how many mathematician it should hire so the ratio will become 10/11
:
Let m = no. of math guys required to accomplish this
That means there were .2(30) = 6 math guys to start with
 = 
Cross multiply
11(m+6) = 10(m+30)
11m + 66 = 10m + 300
11m - 10m = 300-66
m = 234 math guys needed
:
:
Check:
 =
Question 570706: seven times a number is subtracted from 2 times its reciprcoal. the result is 13 what is the number?
Answer by Maths68(1166) (Show Source):
Question 570103: A basket contains many apples and the apples are divided among six people. One third, one fourth, one eigth, and one fith of the apples are given to the first four people, respectively. The fith person gets ten apples and the sixth person gets one apple. Find the original number of apples in the basket.
I tried the following: Let A = Original number of apples
x = number of apples given
A= 1/3x + 1/4x + 1/8x + 1/5x + 10 + 1
Next I determined the LCD was 120
A = 40/120x + 30/120 + 15/120x + 24/120x + 10 +1
A = (109/120x + 11)*120
120A = 109x + 11
120A - 11 = 109x
120A - 11/109 = x
If I left the x out of the fractions then I got the following
120A = 109 +11
120A = 120
Please solve, show work and show me what I'm doing wrong.
Thanks,
Norm
Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!A basket contains many apples and the apples are divided among six people.
One third, one fourth, one eighth, and one fifth of the apples are given to the first four people, respectively.
The fifth person gets ten apples and the sixth person gets one apple.
Find the original number of apples in the basket.
I tried the following: Let A = Original number of apples
:
You don't need x here.
:
A =  A +  A +  A +  A + 10 + 1
Find the Common denominators of all these fractions, that would be 120, as you said
A =  A +  A +  A +  A + 11
A =  A + 11
Multiply both sides by 120, get rid of the fraction
120A = 109A + 120(11)
120A - 109A = 1320
11A = 1320
A = 1320/11
A = 120 apples total
Question 569571: To determine the number of fish in a lake, a park ranger catches 260 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 20 of them are tagged. Estimate the number of fish in the lake.
Answer by KMST(600)  (Show Source):
You can put this solution on YOUR website!The ratio of total fish to tagged fish in the sample caught at the end is  .
If the fish had time to redistribute throughout the lake after being tagged, you would expect that ratio to be the same for the total of fish in the lake. If no one else has been doing anything with the fish, we expect that the total number of tagged fish in the whole lake is the 260 tagged at the beginning of the problem.
So, we can write the proportion:
and we can solve for the total
--> 
The total number of fish can be estimated as 
Question 569637: Lerato's mom uses 1/4kg of cheese to make snackwiches. his dad puts 1/5kg of cheese on the childrsn's sandwiches for school and he eats 1/20kg of cheese while making the sandwiches. what fraction of the kilogram of cheese is left?
Answer by josmiceli(6789)  (Show Source):
Question 569401: The middle number of seven consecutive even numbers is 1004. What is the first number?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!The middle number of seven consecutive even numbers is 1004. What is the first number?
----
Let the middle even number be 2x:
2x = 1004
1st previous 2x-2 = 1002
2nd previous 2x-4 = 1000
3rd previous 2x-6 = 998
---------------------------------------------------------------
Ans: 998
===================
Cheers,
Stan H.
Answer by Alan3354(21608) (Show Source):
Question 569400: Can someone please help me with this? :
The ratio of men to women in a club is 3:7.There are 50 members of the club. How many are men?
Answer by Alan3354(21608) (Show Source):
You can put this solution on YOUR website!The ratio of men to women in a club is 3:7.There are 50 members of the club. How many are men?
-----------------
3+7 = 10
50/10 = 5
----------
3*5 = 15 men
7*5 = 35 women
Question 568797: a bakery makes marble rye using white,light rye, and darkrye flour. if they use three fourths as much light rye as dark rye but the amount of white flour is 50 % of the amount of dark rye, how much light rye flour is needed to make a 1,000 gram loaf?
Answer by josmiceli(6789) (Show Source):
You can put this solution on YOUR website!Let  = grams of white four used
Let  = grams of light rye flour used
Let  = grams of dark rye flour used
given:
(1) 
(2) 
(3) 
Substitute (1) and (2) into (3)
(3) 
Multiply both sides by 
(3) 
(3) 
(3) 
and
(1) 
(1) 
and
(2)
(2) 
(2) 
333.333 grams of light flour are needed
Question 568373: If y varies inversely with the square of x, how is y affected if x is increased by 150%?
Answer by Edwin McCravy(6938)  (Show Source):
You can put this solution on YOUR website!If y varies inversely with the square of x, how is y affected if x is increased by 150%?
y BEFORE = 
y AFTER = 
Now
x AFTER = 150% OF 
x AFTER = 1.5
y AFTER =
y AFTER =  =  =
=  =
=  =
= y BEFORE
So it has been reduced by or  %
Edwin
Question 568298: 95% of h is 60. What is h?
Answer by nerdybill(5412)  (Show Source):
Question 568301: 95% of h is 60. What is h?
Answer by TutorDelphia(189)  (Show Source):
Question 567937: One L of paint is needed to paint a statue 3m high. Find the number of L it will take to paint (to the same thickness) 540 statues similar to the original but only 1 m high.
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!One L of paint is needed to paint a statue 3m high. Find the number of L it will take to paint (to the same thickness) 540 statues similar to the original but only 1 m high.
----
amt. of paint, height, and # of statues are all directly related:
p = k*h*n
Solve for "k" using "One L of paint is needed to paint a statue 3m high".
1 = k*3*1
k = 1/3
------
Equation:
p = (1/3)*h*n
--
Find the number of L it will take to paint (to the same thickness) 540 statues similar to the original but only 1 m high.
p = (1/3)*1*540
paint = 180 L (amt. of paint required)
===========================================
Cheers,
Stan H.
==================
Question 567890: HAE'S book store took in $633.75 at a 35% off sale. what was the original cost of his books? (hint: the selling price is what percent of the original price?)
Answer by Theo(2978) (Show Source):
You can put this solution on YOUR website!let x = original cost of the books.
x - .35x = 633.75
factor to get:
x * (1-.35) = 633.75
simplify to get:
.65 * x = 633.75
divide both sides by .65 to get:
x = 633.75 / x
simplify to get:
x = $975.00
Question 567730: At Pizza Delight in Halifax the prices are:
(i) one 6” pizza for $4.99
(ii) two 6” pizza for $7.49, .1326
(iii) one 9” pizza costs $7.99. .125595
Which are the best and the worst deal.
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!At Pizza Delight in Halifax the prices are:
(i) one 6” pizza for $4.99
--
Area = (pi)3^2 = 9pi sq inches ; price per sq.in = 499/(9pi) = 17.65 cents
--------------------------------------------------
(ii) two 6” pizza for $7.49,
Area = 2*9pi = 18pi sq inches ; price per sq.in = 749/(18pi) = 13.25 cents
------------------------------------------------------
(iii) one 9” pizza costs $7.99.
Area = (4.5)^2(pi) = 20.25(pi) sq. in. : ppsi = 799/(20.25pi) = 12.56 cents
--------------------------
Which are the best and the worst deal.
Best is one 9"
Worst is one 6"
=========================
Cheers,
Stan H.
===========
Question 567451: 1)Borrowed $27,000 from the bank by signing a 9%, 30-day note
2)Paid the note to the bank at maturity.
How Do I calculate the percentage that is on the note?
I'm not getting the correct answer. I keep getting 202.50 in interest when the answer states it's 199.73 in interest.
Answer by scott8148(5895) (Show Source):
You can put this solution on YOUR website!using a 365 day year gives the 199.73, using a 360 day year gives your result
I am not a financial person, so I don't know the different year-length reasons
Question 567386: 8% of what number is 72?
Found 2 solutions by Alan3354, Maths68:
Answer by Alan3354(21608) (Show Source):
Answer by Maths68(1166) (Show Source):
You can put this solution on YOUR website!8% of what number is 72
Let
72 is 8% of x
8%x=72
(8/100)(x)=72
(2/25)(x)=72
2x/25=72
2x=72*25
2x=1800
2x/2=1800/2
x=900
72 is 8% of 900
Question 566805: the reciprocal of two more than a number is three times the reciprocal of the number find the number
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!the reciprocal of two more than a number is three times the reciprocal of the number find the number
-----
Equation:
1/(x+2) = 3(1/x)
Cross-multiply:
----------------------
x = 3(x+2)
x = 3x+6
2x = -6
x = -3
==========
Cheers,
Stan H.
===========
Question 566814: bob, driving a new ford, travels 330 miles in the same amount of time it takes john driving an old chevy and traveling 10 miles per hour faster, to travel 390 miles. how fast is john driving
Answer by solver91311(12126)  (Show Source):
Question 566724: If an item costs 75 cents and it is marked up to 90 cents, what percent mark up would that be?
Answer by Alan3354(21608) (Show Source):
You can put this solution on YOUR website!If an item costs 75 cents and it is marked up to 90 cents, what percent mark up would that be?
-----------
90 - 75 = 15 cents
15/75 = 0.2
x100 = 20%
Question 565982: A tsunami destroyed 4/5 of a forest. If 10,800 trees were lost how many trees survived?
Answer by ad_alta(170)  (Show Source):
Question 565467: Mary receives a 3% commision on every house she sells. If she received a commission of $8571.00, what was the value of house sold?
Write the algebraic expression that models the question.
Solve.
State the equation and solution.
Thanks
Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!Mary receives a 3% commission on every house she sells.
If she received a commission of $8571.00, what was the value of house sold?
Write the algebraic expression that models the question.
:
Let x = the value of the house sold
:
.03x = 8571
:
You should be able to find x (just divide both sides by .03)
Question 565558: A softball team won 84% of the games they played last season. If they played 25 games, how many games did they win?
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!A softball team won 84% of the games they played last season. If they played 25 games, how many games did they win?
-------------------------------------------------
Ans: 0.84*25 = 21 wins
==========================
Cheers,
Stan H.
===========
Question 565319: Steve and Robin have 16 cousins. Steve has 3 times as many as Robin. How many cousins does Steve have?
I know the answer is 12 but how do I solve this so my son (and I) understand?
Sons 5th grade math is stumbling Dad!
Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!let s = no. of Steve's cousins
let r = no. of Robin's cousins
:
Write a simple equation for each statement:
:
Steve and Robin have 16 cousins.
s + r = 16
:
Steve has 3 times as many as Robin.
s = 3r
:
In the 1st equation we can replace s with 3r
3r + r = 16
4r = 16
r = 16/4
r = 4 cousins for Robin
then we know s = 3r, therefore
s = 3*4
s = 12 cousins for Steve
:
Of course they should add up to 16 which they do
Question 565218: John's sales for the week totaled $9,271.43, a 6.5% increase over his sales the previous week. What were his previous week's sales?
Answer by rfer(10432) (Show Source):
Question 565029: Two fractions have the same numerator, but different denominators. Is the fraction with the greater denominator greater than or less than the fraction with the lesser denominator?
Answer by ad_alta(170) (Show Source):
You can put this solution on YOUR website!Think of it this way: numbers in the denominator are what we're dividing by. So in the fraction with the greater denominator, we are splitting the numerator into smaller pieces. The fraction with the greater denominator is therefore less than the other fraction.
Question 564943: Jeff, Tom, and Chelsea order a large pizza. They decide to split the cost according to how much they will eat. Tom pays $6.63, Chelsea eats 1/8 of the pizza, and Jeff eats 1/2 of the pizza. How much did the pizza cost?
Not sure how to set this up.
Answer by scott8148(5895) (Show Source):
You can put this solution on YOUR website!"Chelsea eats 1/8 of the pizza, and Jeff eats 1/2 of the pizza" ___ 1/2 is 4/8
___ so C and J ate 5/8 of the pizza
___ that means T ate 3 eighths
so 3/8 of the pizza cost $6.63(nicely divisible by 3)
Question 564656: How many gallons of 60% antifreeze solution must be mixed with 70 gallons of 15% antifreeze to get a mixture of 50% antifreeze.
Answer by mananth(10554)  (Show Source):
You can put this solution on YOUR website!------------------------percent ---------------- quantity
Antifreeze type I 15----------------70 gallons
Antifreeze type II 60----------------x gallons
Mixture 50----------------70+x gallons
15*70+60x=50(70+x)
1050+60x=3500+50x
60x-50x=3500-1050
10x=2450
/ 10
x= 245 gallons of Antifreeze type II
m.ananth@hotmail.ca
Question 564359: The account executive earns $600 dollars a month, plus 3% commission on sales, The executives goal is to earn $2400 this month, How much must she sell to achieve this goal.
Answer by ad_alta(170) (Show Source):
You can put this solution on YOUR website!Let the salary 'S' be given by S=600+0.03*C for 'C' the sales for which the executive gets commission. We would like to solve 2400=600+0.03*C. The sales, 'C,' come to $60,000. Quite a sum!
Question 563043: There are 7 same-sized cups filled with water which will be used for watering plants. Fred used 1/3 of each cup of water. Janice used 1/4 of each cup of water. Approximately how many cups of water remain?
Answer by bailey13(1)  (Show Source):
You can put this solution on YOUR website! i drew 7 cups then split them into thirds. then shaded in 1/3. after that i made it into fourths by cutting the shaded piece in half. finally i counted the parts unshaded. that left me with 14 parts of the cups of water. so then since the cups were in fourths for every 4 parts that was one cup. so that left me with
3 2/4 cups of water
Question 562879: If a hen and a half,
Lays an egg and a half,
In a day in a half,
How many eggs will six hens lay I seven days?
I came up with 21. 6*1 1/2=4*7=21
Is this right?
Found 2 solutions by Alan3354, fcabanski:
Answer by Alan3354(21608) (Show Source):
You can put this solution on YOUR website!If a hen and a half,
Lays an egg and a half,
In a day in a half,
How many eggs will six hens lay I seven days?
I came up with 21. 6*1 1/2=4*7=21
Is this right?
------------------
If a hen and a half,
Lays an egg and a half,
In a day in a half,
--> 1 hen lays 1 egg in 1.5 days
6 hens lay 6 eggs in 1.5 days
6 hens lay 6*(7/1.5) eggs in 7 days
= 28 eggs
--------------
or,
1.5 eggs = 1.5 hens*1.5 days = 2.25 hen-days
1 egg = 1.5 hen-days --> 1 hen-day = 2/3 eggs
6 hen*7 days = 42 hen-days
42*(2/3) = 28 eggs
Answer by fcabanski(385) (Show Source):
You can put this solution on YOUR website!Use ratios.
Start with 1.5 hens laying 1,5 eggs in 1.5 days. How many eggs do 1.5 hens lay in 1.5 days.
1.5/1.5 = x/1 |cross multiply
1.5x=1.5 so x = 1
1.5 hens lay 1 egg per day. How many eggs does 1 hen lay per day?
1.5/1 = 1/x | cross multiply
1.5x = 1 so x =1/1.5 = .666666666666667 = 2/3. Each hen lays 2/3 egg per day.
6 hens lay 6*2/3 = 12/3 = 4 eggs per days.
That's 7*4 = 28 eggs in 7 days.
If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com
Question 562378: Maya and Kavitha each were paid m dollars in advance to do a certain job together.Maya worked on a job for 20 hrs and Kavitha worked 4hrs less than Maya. If Kavitha gave Maya n dollars of payment so that they would recieve the same hourly wage,what was the dollar amount in terms of n that Maya was paid in advance
Answer by ankor@dixie-net.com(12704) (Show Source):
You can put this solution on YOUR website!Maya and Kavitha each were paid m dollars in advance to do a certain job together.
Maya worked on a job for 20 hrs and Kavitha worked 4hrs less than Maya.
If Kavitha gave Maya n dollars of payment so that they would receive the same hourly wage, what was the dollar amount in terms of n that Maya was paid in advance
:
 = M's hourly wage
 = K's hourly wage
:
Understand that K gives M n dollars to equalize the hourly wage, therefore
 = 
Cross multiply
20(m-n) = 16(m+n)
20m - 20n = 16m + 16n
20m - 16m = 16n + 20n
4m = 36n
Divide both sides by 4
m = 9n dollars paid each in advance
Question 562706: A coat is on sale at a 20% discount. Find the sale price if it's normally $79.
Answer by rfer(10432) (Show Source):
Question 562480: The value of a property declines every year by 5%. Presently, its value is $350,000. What will be its value 4 years from now?
Found 2 solutions by Sarpi, stanbon:
Answer by Sarpi(25)  (Show Source):
You can put this solution on YOUR website!Value of a Property.
Let the timing be: t = 0,1,2,3,4,5 (in years)
Value at t=0 is $350,000
Depreciation rate = 5%
Therefore what will be value at t=4?
Long calculation:
0; 350,000
1; 350,000 - (350,000*5%) = 332,500
2; 332,500 - (332,500*5%) = 315,875
3; 315,875 - (315,875*5%) = 300,081.25
4; 300,081.25 - (300,081.25*5%) = 285,077.1875
5; 285077.1875-(285077.1875 *5%) = 270,823.3281
Short Calculation (using the compounding formula)
Amount = Principal(1+Rate)^time
so here; principal is the initial value = $350,000
Rate is a declining rate, so -5%
time = 4yrs
A = 350,000 * (1-5%)^4
A = 350,000 * (0.95)^4
A = 285,077.1875
Hence the value 4 years from now will be $285,077.19 (rounded to 2 decimal)
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!The value of a property declines every year by 5%. Presently, its value is $350,000. What will be its value 4 years from now?
-------------------
end of 1st year: 0.95*350,000
end of 2nd year: 0.95^2*350,000
end of 3rd year: 0.95^3*350,000
end of 4th year: 0.95^4*350,000 = 285077.19
=====================
Cheers,
Stan H.
=====================
Question 562462: how many 50 dollar bills do you need for 1800$?
Answer by MathHelper7(6)  (Show Source):
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050
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