Questions on Word Problems: Numbers, consecutive odd/even, digits answered by real tutors!

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Tutors Answer Your Questions about Numbers Word Problems (FREE)


Question 571297: one number is seven more than twice another. if their sum is decreased by ten, the result is twelve. find the numbers.
Answer by lwsshak3(2907) About Me  (Show Source):
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one number is seven more than twice another. if their sum is decreased by ten, the result is twelve. find the numbers
**
let x=one of the numbers
2x+7=other numberr
..
x+2x+7-10=12
3x=15
x=5
ans:
numbers are 5 and 17


Question 570798: I am less than 20.
I am more than 13.
I am less than 17.
I am 4 more than 12.
What number am I?

Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
"I am 4 more than 12" --> 16

That wasn't too hard, was it?


Question 571120: Center City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1225 cars, find the capacity for each garage.
Answer by josmiceli(6769) About Me  (Show Source):
You can put this solution on YOUR website!
Let capacity of CCWPG = +c+
Capacity of CCEPG = +c+%2B+251+
given:
+c+%2B+c+%2B+251+=+1225+
+2c+=+1225+-+251+
+2c+=+974+
+c+=+487+
+c+%2B+251+=+738+
Capacity of CCWPG = 487 cars
Capacity of CCEPG = 738 cars


Question 571089: The difference of two numbers is 57. The larger number is three less than six times the smaller number. Find the numbers.
Answer by rfer(10417) About Me  (Show Source):
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(6x-3)-x=57
5x-3=57
5x=60
x=60/5
x=12
6x-3=69


Question 571110: the sum of three consecutive integers is 165. what are the three integers?
Answer by josmiceli(6769) About Me  (Show Source):
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call the integers n, n%2B1, and n%2B2
given:
+n+%2B+n+%2B+1+%2B+n+%2B+2+=+165+
+3n+%2B+3+=+165+
+3n+=+162+
+n+=+54+
+n+%2B+1+=+55+
+n+%2B+2+=+56+
The numbers are 54, 55, and 56
check:
+n+%2B+n+%2B+1+%2B+n+%2B+2+=+165+
+54+%2B+55+%2B+56+=+165+
+165+=+165+
OK


Question 571014: two integers have a mean of 170. the first number is 4 times the second number. find both numbers. I can't figure this problem out please help.
Answer by ankor@dixie-net.com(12681) About Me  (Show Source):
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Two numbers, a & b
Write an equation for each statement:
:
"two integers have a mean of 170."
%28a%2Bb%29%2F2 = 170
a + b = 2(170)
a + b = 340
:
"the first number is 4 times the second number."
a = 4b
:
In the 1st simplified equation, substitute a with 4b
4b + b = 340
5b = 340
b = 340/5
b = 68
:
Find a
a = 4(68)
a = 272
:
:
You can confirm this by finding the mean of these two numbers



Question 571059: the sum of of two consecutive integers is the sum of 389. What is the larger integer?
Answer by stanbon(48502) About Me  (Show Source):
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the sum of of two consecutive integers is the sum of 389.
What is the larger integer?
----------------------
1st: x
2nd: x+1
---
sum = 389
2x+1 = 389
2x = 388
x = 144
x+1 = 145
===============
Cheers,
Stan H.
===============


Question 570940: Four increased by double the difference of a number and six
Answer by nyc_function(2626) About Me  (Show Source):
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Answer: 2(x - 6) + 4


Question 571037: a car dealer sells a car for 39,000, which represents 25% markup over the dealer's cost. What was the cost of the SUV to the dealer?
Answer by rfer(10417) About Me  (Show Source):
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39000/1.25=$31,200


Question 570918: One number is four less than three times another. If their sum is increased by five, the result is twenty-five. Find the numbers?
Answer by Maths68(1140) About Me  (Show Source):
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Let
larger number = x
smaller number = y

One number is four less than three times another
x=3y-4........(1)
If their sum is increased by five, the result is twenty-five
x+y+5=25
x+y=25-5
x+y=20............(2)
Put the value of x from (1) to (2)
3y-4+y=20
4y=20+4
4y=24
4y/4=24/4
y=6
Put the value of y in (1)
x=3y-4........(1)
x=3(6)-4
x=18-4
x=14
Numbers are 14 and 6


Question 570911: the room number of two adjacent classrooms are two consecutive even numbers if their sum is 1058 what are the even numbers
Answer by josmiceli(6769) About Me  (Show Source):
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Call the lowest number +n+
The next higher even number is +n+%2B+2+
given:
+n+%2B+n+%2B+2+=+1058+
+2n+=+1058+-+2+
+2n+=+1056+
+n+=+528+
+n+%2B+2+=+530+
The classroom numbers are 528 and 530
check:
+528+%2B+530+=+1058+
+1058+=+1058+
OK


Question 570891: 4 consecutive whole numbers such that the sum of the first three equals the fourth number
Answer by stanbon(48502) About Me  (Show Source):
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4 consecutive whole numbers such that the sum of the first three equals the fourth number
----
1st: x-2
2nd:x-1
3rd:x
4th:x+1
----
sum = 3(x+1)
4x-2 = 3x+3
x = 5
---
1st: x-2 = 3
2nd: x-1 = 4
3rd: x = 5
4th: x+1 = 6
-----------------
cheers,
Stan H.


Question 570886: THE DIFFERENCE BETWEN 3 TIMES A NUMBER AND 11 IS 10
Answer by stanbon(48502) About Me  (Show Source):
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THE DIFFERENCE BETWEN 3 TIMES A NUMBER AND 11 IS 10
------------
Let the number be "x":
Equation:
3x-11 = 10
3x = 21
x = 7
===============
Cheers,
Stan H.


Question 570849: Three times a number is 36 more than twice the number. How do I write this. Im confused. I tried 3x+36=2x
Found 2 solutions by JBarnum, mananth:
Answer by JBarnum(1826) About Me  (Show Source):
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three times a number (3n)
is (=)
36 more than (36+)
twice the number (2n)
3n=36%2B2n

Answer by mananth(10539) About Me  (Show Source):

Question 570838: One integer is 3 less than another. The sum of their squares is 65. find the integers.
Answer by JBarnum(1826) About Me  (Show Source):
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a=b-3
a%5E2%2Bb%5E2=65
.
%28b-3%29%5E2%2Bb%5E2=65
b%5E2-6b%2B9%2Bb%5E2=65
2b%5E2-6b%2B9=65
2b%5E2-6b-56=0
2%28b%5E2-3b-28%29=0
find two numbers that multiply to get -28 and add to get -3
-7 and 4
2%28b-7%29%28b%2B4%29=0
b=7,-4
plug the b's into the first equation
a=4,-7
if you cant understand the quick solve above there's always the long quadratic solution below
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 1b%5E2%2B-3b%2B-28+=+0) has the following solutons:

b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-28=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+121+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+7
b%5B2%5D+=+%28-%28-3%29-sqrt%28+121+%29%29%2F2%5C1+=+-4

Quadratic expression 1b%5E2%2B-3b%2B-28 can be factored:
1b%5E2%2B-3b%2B-28+=+1%28b-7%29%2A%28b--4%29
Again, the answer is: 7, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-28+%29




Question 570684: The difference between two numbers is 12, and four times the
Langer number exceeds three times the smaller number by 90,what is the larger number?

Answer by Maths68(1140) About Me  (Show Source):
You can put this solution on YOUR website!
Let
Larger number = x
Smaller number = y
Given
======
The difference between two numbers is 12
x-y=12
x=12+y..................(1)
Four times the larger number exceeds three times the smaller number by 90
4x=3y+90...........(2)
Put the value of x from (1) to (2)
4x=3y+90
4(12+y)=3y+90...........(2)
48+4y=3y+90
4y-3y=90-48
y=42
Put the value of y in (1)
x=12+y
x=12+42
x=54

Larger Number is 54


Question 570453: find four consecutive whole numbers such that the sum of the first three numbers equal the fourth number.
Answer by ankor@dixie-net.com(12681) About Me  (Show Source):
You can put this solution on YOUR website!
Only 0, 1, 2, 3 would accomplish this


Question 570457: what is the equation for; 3 times the difference of the square of a number and 1 is 72
Answer by ankor@dixie-net.com(12681) About Me  (Show Source):
You can put this solution on YOUR website!
what is the equation for; 3 times the difference of the square of a number and 1 is 72
:
Write what it says
3(x^2-1) = 72
3x^2 - 3 = 72
3x^2 = 72 + 3
3x^2 = 75
divide both sides by 3
x^2 = 25
x = 5
:
Check this
3(5^2-1) = 72


Question 570423: The sum of four consecutive odd numbers is 224. Find the numbers.
Answer by Alan3354(21546) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of four consecutive odd numbers is 224. Find the numbers.
---------
224/4 = 56, the middle
--> 53, 55, 57 & 59


Question 570426: I am a 3-digit number that is even. My hundreds and ones digits are the same and have a sum of 10. My tens digit is 2 less than my ones digit. What number am I?
Answer by solver91311(12116) About Me  (Show Source):
You can put this solution on YOUR website!


Not possible. The only identical pair of single digits that sum to 10 are 5 and 5. But that means the ones digit is 5, but 5 is odd, but the 3 digit number can only be even if the ones digit is even.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 570397: three more than twice a number is greater than negative thirteen. find all numbers that make this statement true.
Answer by rfer(10417) About Me  (Show Source):
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2x+3=-13
2x=-13-3
2x=-16
x=-8


Question 570353: what 3 digit number has it's last 2 digits the same and the sum of it's digits equals 26???
Answer by Alan3354(21546) About Me  (Show Source):
You can put this solution on YOUR website!
what 3 digit number has it's last 2 digits the same and the sum of it's digits equals 26???
------------
899
PS it's = it is


Question 570273: If I add the square of a number to the number itself, I get 30. What could the number be?
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
n^2+n=30
n^2+n-30=0
(n-5)(n+6)=0
n= 5 or -6


Question 570229: Three consecutive odd integers are such that the sum of four times the first and the second is three times the third.
Answer by josmiceli(6769) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive odd integers be
+n+, +n+%2B+2+, and +n+%2B+4+
given:
+4n+%2B+n+%2B+2+=+3%2A%28+n+%2B+4+%29+
+5n+%2B+2+=+3n+%2B+12+
+2n+=+10+
+n+=+5+
+n+%2B+2+=+7+
+n+%2B+4+=+9+
The integers are 5, 7, and 9
check:
+4n+%2B+n+%2B+2+=+3%2A%28+n+%2B+4+%29+
+4%2A5+%2B+5+%2B+2+=+3%2A%28+5+%2B+4+%29+
+20+%2B+7+=+3%2A9+
+27+=+27+
OK


Question 570173: If the sum of an integer and 7 is multiplied by 3, the result is 6 times the original number? What's the integer?
Answer by stanbon(48502) About Me  (Show Source):
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If the sum of an integer and 7 is multiplied by 3, the result is 6 times the original number? What's the integer?
----
Equation:
3(x + 7) = 6x
Divide both sides by 3:
x+7 = 2x
x = 7
======
Cheers,
Stan H.


Question 569522: If there are (2n+1) terms in an arithmetic series, prove that the ratio of the sum of odd place terms to the sum of even place terms is +n%5E4-1+ : +n%5E4-n%5E3%2Bn%5E2-n+ .
Answer by richard1234(4789) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose our sequence is a, a+d, a+2d, ..., a+2nd (this ensures that there are 2n+1 terms). Denote S_o and S_e to be the sum of the odd place terms and even place terms respectively. Then,





S_o includes n+1 terms and S_e includes n terms. By equating the coefficients of a and d in each series, we have





Therefore, . Multiplying both numerator and denominator by n^3 - n^2 + n - 1 yields the desired result.


Question 570015: the quotient of two numbers is 8,the difference of the same two numbers is 49. what are the two numbers?

Answer by solver91311(12116) About Me  (Show Source):
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"Quotient" is the result of division, so:



must be greater than since the quotient above is greater than 1, so:



Multiply both sides of the first equation by , then substitute the RHS expression into the second equation. Solve for , then calculate using either of the equations.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 569960: the sum of two numbers is 53. the first number is 137 more than the second number. Find the numbers

Answer by rfer(10417) About Me  (Show Source):
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x+x+137=53
2x=53-137
2x=-84
x=-84/2
x=-42
---------------
x+137=-42+137=95
x=-42


Question 569673: The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers.
Answer by htmentor(580) About Me  (Show Source):
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The sum of reciprocals of two consecutive even numbers is 5/12,find the numbers.
=============
Let n = the smaller number
Then n+2 = the other number
Given: sum of the reciprocals is 5/12
1/n + 1/(n+2) = 5/12
((n+2)+n)/(n(n+2)) = 5/12
Cross-multiply and collect terms:
12(2n+2) = 5n(n+2)
This gives 5n^2 - 14n - 24 = 0
This expression can be factored as
(5n+6)(n-4) = 0
This gives n = -6/5 [not an integer] and n = 4
So the two numbers are 4 and 6


Question 569737: a basketball player scored 19 times during one game. She scored a total of 37 points ,two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
Answer by JBarnum(1826) About Me  (Show Source):
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(t) two point shot
(f) free throw
t%2Bf=19
2t%2Bf=37
t=19-f
2%2819-f%29%2Bf=37
38-f=37
f=1
t=18
check
18+1=19
correct
36+1=38
correct


Question 569620: What is the shortest piece of rope i would be able to divide into lengths of 4m ,6m and 9m without having to throw away any of the rope? Also state how many pieces of each length there must be.
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(21546) About Me  (Show Source):
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What is the shortest piece of rope i would be able to divide into lengths of 4m ,6m and 9m without having to throw away any of the rope? Also state how many pieces of each length there must be.
--------------
36 meters
---
36/4 = 9 pieces, etc.

Answer by josmiceli(6769) About Me  (Show Source):
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I think it's +108+ m
+108%2F4+=+27+ pieces of 4 m lengths
+108%2F6+=+18+ pieces of 6 m lengths
+108%2F9+=+12+ pieces of 9 m lengths
I noticed that +54+ won't work since
+54%2F4+=+13.5+


Question 569685: the sum of two numbers in 10. the first number is 2/3 of the second number. what are the numbers
Answer by JBarnum(1826) About Me  (Show Source):
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F=first number S=second number
F%2BS=10
F=%282%2F3%29S
%282%2F3%29S%2BS=10
%285%2F3%29S=10
5S=30
S=6


Question 15090: One and two thirds of a number equals one and a half. What is the number?
Answer by jimbob2(1) About Me  (Show Source):
You can put this solution on YOUR website!
Person who answed this must have missread secound part, it says it equals one and a half, not one half. The correct answer is 9/10 using the same logic.


Question 569343: Find the smallest number that meets all of these conditions.
when you divide the number by 5 there are 3 left over
when you divide the number by 8 there are 2 left over
when you divide the number by 9 there are 4 left over

Answer by AnlytcPhil(1116) About Me  (Show Source):
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>>...when you divide the number by 9 there are 4 left over...<<
That says the number has to be 4 more than a multiple of 9

The multiples of 9 are

{9,18,27,36,45,54,63,72,81,90,...}

The numbers which are 4 more than a multiple of 9 are

Possible answers: {13,22,31,40,49,58,67,76,85,94,...}

So the number must be one of those.

>>...when you divide the number by 8 there are 2 left over...<<

That says the number has to be 2 more than a multiple of 8

The multiples of 8 are

{8,16,24,32,40,48,56,64,72,80,88,96}

The numbers which are 2 more than a multiple of 8 are

Possible answers: {10,18,26,34,42,50,58,66,74,82,90,98}

So the number must be one of those.

The only number common to both sets of possible answers is 58.  However
we only took the numbers up to 100.  It may be that there would be other
numbers is common if we took higher numbers.  But let's see if 58 satisfies 
the other requirement. If not we'll have to get more elements of those
sets.

>>...when you divide the number by 5 there are 3 left over...<<
That's true of 58 because it's 3 more than 55 which is a multiple of 5.
So we didn't have to go higher to find the answer.

Answer: 58.

Edwin


Question 569320: What is another way you can model 7 snack packs containing 6 crackers each? What does model mean? Thank you. 3 graders homework that mom and dad are confused.
Answer by solver91311(12116) About Me  (Show Source):
You can put this solution on YOUR website!


If you are asking about "another way," then there must be an example already done. What does that look like? We would be delighted to help, but you have to tell the whole story.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 569171: what is the lagest 4 digit even number you can make with the numbers 1234?
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
what is the lagest 4 digit even number you can make with the numbers 1234?
Ans: 4312


Question 568951: a number is 5 less than three times another number. the sum of two numbers is 31. Wat r d numbers?
Answer by Maths68(1140) About Me  (Show Source):
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Let
x = larger number
y = smaller number

Given
The sum of two numbers is 31
x+y=31
x=31-y..........(1)
A number is 5 less than three times another number
x=3y-5..........(2)
Put the value of x from (2) to (1)
3y-5=31-y
3y+y=31+5
4y=36
4y/y=36/4
y=9
Put the value of y in (1)
x=31-y
x=31-9
x=22
Numbers are 22 and 9


Question 568674: what are rational numbers
Answer by KMST(576) About Me  (Show Source):
You can put this solution on YOUR website!
Rational numbers are numbers that can be written as a ratio of two integers
2=2%2F1, -8=%28-8%29%2F1, 3%2F4, and -2%2F5=%28-2%29%2F5 are rational numbers.
sqrt%283%29, 7%2Bsqrt%282%29 and pi are not rational numbers. They are called irrational numbers. The irrational numbers, together with the rational numbers, make up the real numbers.


Question 568600: This is for my daughter.
The question is I am thinking of two whole numbers. The second is larger than the first. The sum of the squares of the numbers is 61.What are the two numbers? Explain how you came up with that answer. Thanks

Answer by Alan3354(21546) About Me  (Show Source):
You can put this solution on YOUR website!
The question is I am thinking of two whole numbers. The second is larger than the first. The sum of the squares of the numbers is 61.What are the two numbers? Explain how you came up with that answer. Thanks
--------------
61 - 1 = 60, not a perfect square
61 - 4 = 57, "
61 - 9 = 52, "
61 - 16 = 45 "
61 - 25 = 36 --> 5 & 6
--------------------
Works for small numbers


Question 568555: find three consecutive odd numbers whose sum is 303

Answer by bucky(2097) About Me  (Show Source):
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Consider a series of odd numbers such as 1, 3, 5, 7, 9, 11 and so on. This series consists of consecutive odd numbers because no odd number is left out. Now, notice the particular feature of this series is that each number is 2 greater than the number that comes just before it. So if 5 is the first odd number you select, the next consecutive odd number is 5 + 2 or 7. And think about this. The next consecutive number after that is two more than its predecessor, so it is 7 + 2 or 9. But 7 is equal to 5 + 2. So we can say that the third number in this series of consecutive odd numbers is (5 + 2) + 2 = 5 + 4 = 9. In fact we can write the series of consecutive odd numbers starting with 5 as (5), (5 + 2), (5 + 4), (5 + 6), (5 + 8), and so on.
.
In general we can similarly write the series of odd numbers in which n represents the unknown first number, as n, n+2, n+4, n+6, n+8, ...
.
So three consecutive odd numbers can be written as n, n+2, and n+4. The problem asks you to find three consecutive odd numbers whose sum is 303. You can set up the equation for the sum of three consecutive odd numbers as equal to 303 by writing it as follows:
.
n + (n+2) + (n+4) = 303
.
You can now simplify the left side by adding the three n terms to get 3n and then adding the 2 and the 4 to get 6. This makes the equation become:
.
3n + 6 = 303
.
First get rid of the 6 on the left side by subtracting 6 from both sides to simplify the equation to:
.
3n = 297
.
Solve for n by dividing both sides of the equation by 3 (the multiplier of x) to reduce the equation to:
.
n = 99
.
We identified n as the first term in the series. So the second consecutive odd term must be 2 more that 99, or it must be 101. And the third consecutive odd term must be 2 more than the second term, so it must be 103.
.
Check the answer by adding 99 + 101 + 103 to ensure that the sum of these three consecutive odd numbers is 303, just as the problem requires it to be.
.
In summary, the 3 consecutive odd numbers that add to a total of 303 are 99, 101, and 103.
.
I hope this helps you to understand how to work problems having consecutive odd numbers.
.


Question 568494: THE DIFFERENCE between 54 tens and the largest 2 digit number is?
Answer by AnlytcPhil(1116) About Me  (Show Source):
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THE DIFFERENCE between 54 tens and the largest 2 digit number is
54 tens means 54 times 10 which is 540

The largest 2 digit number is 99

So the problem asks for the difference between 540 and 99.

To find the difference between a first number and a second number,
you subtract:  first number - second number.

            540 - 99 = 441

Edwin


Question 568497: THE DIFFERENCE between 54 tens and the largest 2 digit number is
Answer by AnlytcPhil(1116) About Me  (Show Source):
You can put this solution on YOUR website!
THE DIFFERENCE between 54 tens and the largest 2 digit number is
54 tens means 54 times 10 which is 540

The largest 2 digit number is 99

So the problem asks for the difference between 540 and 99.

To find the difference between a first number and a second number,
you subtract:  first number - second number.

            540 - 99 = 441

Edwin


Question 568454: the sum of two numbers is 32. one of the numbers is 4 less than 5 times the other. find the two numbers
Answer by solver91311(12116) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent one of the numbers.

Let represent the other.

You are given that:



and



Solve the 2X2 system by substitution.

John

My calculator said it, I believe it, that settles it
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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, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730