Tutors Answer Your Questions about Problems-with-consecutive-odd-even-integers (FREE)
Question 572737: Can you please help me and show me how to translate this problem?
Twice the sum of two consecutive odd integers is 32. Find the integers.
Answer by josmiceli(6797)   (Show Source):
Question 572496: please help me solve the following:
find three consecutive odd integers whose sum is equal to five more than two times the second largest number among the three integers.
Answer by Maths68(1166)  (Show Source):
You can put this solution on YOUR website!Let
Smaller number = x+1
Larger number = x+3
Largest number = x+5
x+1+x+3+x+5=2(x+3)+5
3x+9=2x+6+5
3x-2x+9=11
x=11-9
x=2
Smaller number = x+1 = 2+1 = 3
Larger number = x+3 = 2+3 = 5
Largest number = x+5 = 2+5 = 7
Three consecutive odd integers 3, 5, 7
Question 572351: if x represents the first, or smallest, of three consecutive odd intergers, express for in terms of x
Answer by Alan3354(21610)  (Show Source):
You can put this solution on YOUR website!if x represents the first, or smallest, of three consecutive odd intergers, express for in terms of x
==========================
x
Question 571639: what are the even and odd integers respectively?
Answer by Alan3354(21610) (Show Source):
You can put this solution on YOUR website!what are the even and odd integers respectively?
-------------
Even are divisible by 2, such as 2, 4, 6, 8, 10, 998 etc
Odd are the others ones.
------------
Also negative integers, eg, -8 & -100, are even.
Question 571610: . What is the largest natural number by which the product of three consecutive even natural numbers is Always divisible?
Answer by KMST(600)  (Show Source):
You can put this solution on YOUR website!The smallest three consecutive even natural numbers are 2,4,and 6, and their product is 48, so the answer could be 48 or less, but cannot be more than 48 because that would not work for 2, 4, and 6.
For a general case, three consecutive even natural numbers can be represented as
  and 
Their product would be
It is obviously divisible by 8, but there are factors in
  and  that we have to take into account.
At least one of those three numbers is even (maybe just ), so there is and factor 2 in  .
At least one of and is divisible by 3, so there is and extra factor 3 in .
We have the factors 8, 2, and 3, so the product of any three consecutive even natural numbers is always divisible by
Question 569555: Find two consecutive even integers such that the smaller added to three times the larger gives a sum of 30
Answer by KMST(600) (Show Source):
You can put this solution on YOUR website!Let  be the larger even integer. The previous even integer would have been
We know that  , so
-->  -->  --> 
The even integers are 6 and 8
Checking: 
Question 569348: if the first and third of three consecutive odd integers are added, the result is 63 less then five times the second integer. Find the third integer.
Answer by solver91311(12131)  (Show Source):
Question 568294: the sum of two consecutive integers is 138. find the integers.
Answer by TutorDelphia(189)  (Show Source):
You can put this solution on YOUR website!Two consecutive integers will not add up to be an even number since an odd number plus an even number always results in an odd (try it odd 3+4=7; 12+13=25)
I'm guessing you mean the sum of three consecutive integers
lets name our first number n. Our next number in line will be one more than that...so n+1 followed by n+2
all these add up to be 138
so we get
n+(n+1)+(n+2)=138 (the parenthesis don't do anything since this is all addition but help to separate the three consecutive integers)
combine like terms
3n+3=138
subtract 3 from both sides
3n=135
divide both sides by 3
n=45
n+1=46
n+2=47
and 45+46+47=135
so those are your three numbers
Question 567990: Find 3 consecutive even integers whose sum is 186
Answer by Alan3354(21610) (Show Source):
Question 567761: The sum of 4 consecutive even integer equals 7 times the greatest of the integers. Find the integers.
Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!The sum of 4 consecutive even integer equals 7 times the greatest of the integers. Find the integers.
-------
1st: 2x-2
2nd: 2x
3rd: 2x+2
4th: 2x+4
------------------
Equation:
sum = 7(2x+4)
8x+4 = 14x+28
6x = -24
x = -4
-----
1st: 2x-2 = -10
2nd: -8
3rd: -6
4th: -4
---
Check: sum = 7(-4)
-28 = -28
=================
Cheers,
Stan H.
===============
Question 567750: The sum of three consecutive even integers is 234. what are the integers?
Answer by josmiceli(6797) (Show Source):
Question 567318: Find, with proof, all the perfect squares each of which is the product of four consecutive odd natural numbers. (if there is no such combination then show that through a simple proof)
Answer by richard1234(4802)  (Show Source):
You can put this solution on YOUR website!Let k-3, k-1, k+1, k+3 be the four numbers. Then for some integer m,
(k-1)(k+1)(k+3))
(k^2 - 1))
Compare with ^2 = k^4 - 10k^2 + 25) . This is definitely a perfect square, so we need this to differ with m^2 by 16. A simple check shows that {9,25} and {0,16} are the only pairs of perfect squares that differ by 16. {0,16} is impossible because we want our perfect square to be odd. If we have {9,25} then
^2 = k^4 - 10k^2 + 25 = 25)
Hence k^4 - 10k^2 = 0, (k^2)(k^2 - 10) = 0. The only integer solution is k = 0, which yields {-3,-1,1,3}, and m^2 = 9. However, this is not in the set of natural numbers, so there are no solutions.
Question 567230: Two negative integers have a sum of -12 and a product of 11. What are the integers?
Answer by ankor@dixie-net.com(12706)  (Show Source):
Question 567206: find three consecutive odd integers such that three times the middle integer is one more than the sum of the first and the third
Answer by mananth(10554)  (Show Source):
Question 565975: Hello,
please help me solve this equation: Two numbers differ by 2. Twice the smaller number is added to the larger number and the result is 6. Find the numbers.
I have tried solving this equation and i only got this:
Let the smaller number be 'x', and the larger number be 'y'.
x = y - 2 (since they differ by 2)
Equation 1) 2x + y = 6
2(y - 2) + y = 6
2y - 4 + y = 6
3y - 4 = 6
3y = 10
(thats all..)
Answer by ankor@dixie-net.com(12706) (Show Source):
You can put this solution on YOUR website!Two numbers differ by 2. Twice the smaller number is added to the larger number and the result is 6. Find the numbers.
I have tried solving this equation and i only got this:
Let the smaller number be 'x', and the larger number be 'y'.
x = y - 2 (since they differ by 2)
Equation 1) 2x + y = 6
2(y - 2) + y = 6
2y - 4 + y = 6
3y - 4 = 6
3y = 10
Continue
y = 
then
x = y - 2
x = - 2
x = - 
x = 
:
You know what you were doing, but because the solutions were not integers, you doubted.
:
Check our solution in the 2nd equation: 2x + y = 6
2( ) + = 6
(  + = 6
 = 6
6 = 6
Question 566026: Find two consecutive integers such that twice the smaller is 16 more than the larger
Answer by ad_alta(170)  (Show Source):
Question 565645: find the smallest of three consecutive positive integers such that the product of two smaller integers is 68 more than twice the largest integer
Answer by ad_alta(170) (Show Source):
Question 565657: jose and juan went running. joe ran 2 miles less than half as many miles as juan. jose ran 6 miles. how many miles juan run?
Answer by ad_alta(170) (Show Source):
Question 565652: what is the square root of 80
Answer by Alan3354(21610) (Show Source):
Question 565388: PLEASE SHOW ME HOW DID YOU GET THE ANSWER TO THIS - 1) The sum of two numbers is 18. And the sum of their squares is 170. Find the numbers
Answer by josmiceli(6797) (Show Source):
You can put this solution on YOUR website!Call numbers  and 
given:
(1) 
(2) 
-------------------
(1) 
Substitute this into (2)
(2) 
(2) 
(2) 
(2) 
(2) 
(2) 
(2) 
complete the square
(2) 
(2) 
(2) 
Take the square root of both sides
(2) 
(2) 
and, since
(1)
(1) 
(1) 
The numbers are 11 and 7
check:
(2)
(2) 
(2) 
(2) 
OK
Question 565387: the product of two consecutive integers is 16 less than the square of the next larger integer. what are the three integers? PLEASE SHOW ME HOW DID YOU GET THAT ANSWER STEP BY STEP THANKS
Answer by josmiceli(6797) (Show Source):
Question 564968: what is the largest possible product for two odd integers whose sum is 30?
Answer by Alan3354(21610) (Show Source):
You can put this solution on YOUR website!what is the largest possible product for two odd integers whose sum is 30?
----------
225 = 15*15
----------
13*17 = 221
11*19 = 209
etc
n = 0 is the max product
Question 564665: The product of two consecutive positive odd integers is 38 less than the square of the greater integer. Find the integers.
Answer by ad_alta(170) (Show Source):
You can put this solution on YOUR website!Let the first integer be 'n.' Then n(n+2)+38=(n+2)^2. Solve using the quadratic equation: n=17. The two odd integers are 17 and 19.
Question 563258: the difference of 3 times the larger consecutive integer and the smaller consecutive integer is 7
can somebody work this out and show me how you got it ?
Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!the difference of 3 times the larger consecutive integer and the smaller consecutive integer is 7
---
smaller: x
larger: x+1
------------------
Equation:
3(x+1) - x = 7
-----
3x+3-x = 7
2x + 3 = 7
2x = 4
x = 2
=============
Cheers,
Stan H.
=============
Question 563016: how do you do 2x-y=2
-5x+4y=-2 in elimination method
Answer by josmiceli(6797) (Show Source):
You can put this solution on YOUR website!(1) 
(2) 
------------------
Multiply both sides of (1) by 
and add the equations
(1) 
(2)
Plug this back into (1) or (2)
(1) 
(1) 
(1) 
(1) 
(1) 
The solution is (2,2)
Here's the plot of the 2 lines:
Question 562535: the product of two consecutive integers is 5 more than their sum. find the integers.
Answer by solver91311(12131) (Show Source):
Question 561765: Please help me solve this problem:find all sets of tow consecutive positive odd integers whose sum is no greater than 18. I tried 0>x+x+2<18
Answer by ankor@dixie-net.com(12706) (Show Source):
You can put this solution on YOUR website!Solve this problem:
find all sets of two consecutive positive odd integers whose sum is no greater than 18.
:
the phrase "no greater than 18" implies that 18 can be included, therefore
:
x + (x+2) =< 18
2x + 2 =< 18
2x =< 18 - 2
2x =< 16
x =< 16/2
x =< 8
However, they want odd integers, therefore
7, 9 would have to be the highest set
and
5, 7
3, 5
1, 3
Question 561631: The product of two consecutive integers is 5 more than their sum. Find the integers.
Answer by mananth(10554) (Show Source):
You can put this solution on YOUR website!let x & x+1 be the numbers
x(x+1) = x+x+1+5
x^2+x=2x+6
x^2-x-6=0
x^2-3x+2x-6=0
x(x-3)+2(x-3)=0
(x+2)(x-3)=0
x=-2 OR 3
The numbers are
3& 4 OR -2,-1
Question 560711: the sum of the squares of two consecutive even integers is 52. Find the integers.
Answer by richard1234(4802) (Show Source):
You can put this solution on YOUR website!4^2 + 6^2 = 52, so {4,6} works. Additionally {-6,-4} works.
You could solve it algebraically by stating that x^2 + (x+2)^2 = 52, but they're integers and guess-and-check is 100 times easier. Just remember that {-6,-4} also works.
Question 560158: The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
If x represents the smallest integer, then which of the following equations could be used to solve the problem?
Answer by ankor@dixie-net.com(12706) (Show Source):
You can put this solution on YOUR website!The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
:
x = (x+2) + (x+4)
x = 2x + 6
-6 = 2x - x
x = -6
Question 560148: find three consecutive intergers such that the product of the second and third is 56
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(21610) (Show Source):
You can put this solution on YOUR website!find three consecutive intergers such that the product of the second and third is 56
---------------
sqrt(56) =~ 7.5, the middle
--> 7*8 = 56
--> 6, 7 & 8
-9, -8 & -7
Answer by josmiceli(6797) (Show Source):
Question 558319: determine between which consecutive intergers that real zeros of f(x)=x^3-2 are located
Answer by JBarnum(1826)  (Show Source):
You can put this solution on YOUR website!x cant be a negative number or it would be negative + negative which is less than 0
x cant be 2 or more because 2^3= 8 8-2=6 which isnt 0
x cant be 1 or less because 1^3=1 and 1-2 =-1 which isnt 0
so the number has to be between the two consecutive intergers: 1 and 2
and to be exact if your wondering whats exactly x to make the zero it is 1.25992104989487316476...
Question 558257: Hi, if its asking for consecutive odd intergers, is it supposed to be x, x+2, x+4, etc? Also what is it supposed to be for even intergers? Thank you so much! I have a final tomorrow :)
Answer by richard1234(4802) (Show Source):
You can put this solution on YOUR website!You can use x, x+2, x+4, ... for even integers as well (with the condition that x is even -- if you obtain an odd value for x, ignore it).
The more general way to put it is 2x, 2x+2, ... for even integers and 2x+1, 2x+3, ... for odd integers (since x can be *any* integer now).
Question 557820: One number is twice as large as a second number. If the sum of the two numbers is 114, what are the two numbers?
Answer by mananth(10554) (Show Source):
Question 557158: the product of two consecutive odd integers is 77 more than twice the larger, Find the integers please. I cannot set up "product" consecutive integers?
Found 3 solutions by laurien56, stanbon, Alan3354:
Answer by laurien56(2)  (Show Source):
Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!product of two consecutive odd integers is 77 more than twice the larger,
Find the integers.
-------
Equation:
x(x+1) = 2(x+1)+77
-----
x^2+x = 2x+79
x^2-x-79 = 0
------
This quadratic does not have an integer solution.
==============
Cheers,
Stan H.
Answer by Alan3354(21610) (Show Source):
You can put this solution on YOUR website!the product of two consecutive odd integers is 77 more than twice the larger, Find the integers please. I cannot set up "product" consecutive integers?
---------------
The product is x*(x+2)
---
x*(x+2) = 2(x+2) + 77
x^2 + 2x = 2x + 4 + 77
x^2 - 81 = 0
x = ± 9
-------
--> 9 & 11
and -9 & -7
Question 556089: find three consecutive integers such that the product of the first and the second is equal to the product of -6 and the third.
Answer by TutorDelphia(189) (Show Source):
You can put this solution on YOUR website!Three consecutive integers. If we say the first one is n, than the 3 will be n, n+1 and n+2
Therefore we can write the problem as
n*(n+1)=-6*(n+2)
Distribute the n and -6
Add 6n to both sides
add 12 to both sides
factor
(n+3)(n+4)=0
n=-3 or -4
So our integers would be -3,-2,-1
or -4,-3,-2
-3*-2=-1*6
6=6
-4*-3=-2*-6
12=12
Question 555997: Find 3 consecutive integers whose sum is 27?
Answer by Alan3354(21610) (Show Source):
Question 554989: 4 times a number and 5 times the same number added to 75 gives 156. Find the number. ?
Answer by ankor@dixie-net.com(12706) (Show Source):
You can put this solution on YOUR website!4 times a number and 5 times the same number added to 75 gives 156. Find the number. ?
:
4x + 5x + 75 = 156
9x + 75 = 156
Hey, you can do this yourself!
Question 554892: The product of two consecutive odd integers is 63. Find the numbers.
Answer by Alan3354(21610) (Show Source):
Question 554807: Find two consecutive integers whose sum is 27
Answer by nyc_function(2645)  (Show Source):
Question 554673: w minus negative 3 equals negaative 2, what is w?
Answer by jim_thompson5910(21685) (Show Source):
Question 552828: How do I solve this? ::: Find three consecutive odd integers such that the sum of two times the first and four times the third is four more than six times the second.
Answer by stanbon(48569) (Show Source):
You can put this solution on YOUR website!How do I solve this? ::: Find three consecutive odd integers such that the sum of two times the first and four times the third is four more than six times the second.
----
1st: 2x-1
2nd: 2x+1
3rd: 2x+3
-----------
Equation:
2(2x-1)+4(2x+3) = 6(2x+1)+4
--------------------------------
4x-2+8x+12 = 12x+10
12x + 10 = 12x + 10
----
This is an identity.
x can be any Real Number
===========================
Cheers,
Stan H.
=====================
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