The sum of two consecutive odd integers is 60. What are the integers?

How to solve an algebra word problem consecutive integers.
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[@stevenjohnson1143]

Simple 29 and 31

[@jrkorman]

To get an algebraic expression I used (x + 1) + (x - 1) = 60 x + 1 + x -1 = 60; 2x = 60; x = 30 x + 1 = 31; x - 1 = 29

[@henkhu100]

You write that x is the sum of two even numbers equal to 60 so 30 (that is the value of x) is the sum of two even numbers equal to 60? The method is correct, but your text does not make sense.

[@henkhu100]

@user-ky5dy5hl4d Both methods are correct. If you will have to find two values with a difference of two you can name the values x and x+2. or x and x-2. or x-1 and x+1 Then you use the criteria (sum = 60) and find the x and so the two values. using x and x+2 gives x=29. with solutions 29 and 31 using x and x-2 gives x=31 with solutions 29 and 31 using x-1 and x+1 gives x=30 with solutions 29 and 31 That is the normal way to solve a problem like this. Why is it a trick? How do you solve the problem without this "trick"?

[@diz354]

A video of math vocabulary would be helpful for anyone who’s relearning math.

[@dwaipayandattaroy9801]

Evens - 28, 32, Odds 29,31 Equals 30, 30 Unequal 10,50 11, 49 19,41 Bacic maths

[@dwaipayandattaroy9801]

✌✌My calculations too complicated, these solvings are bichy , chill basic ✌✌

[@Herlongian]

You can also use x-2 for a consecutive odd integer.

[@robertakerman3570]

Trial & error also could work. It was fun.

[@devonwilson5776]

Greetings. The numbers are 29 and 31. We need to find conservative odd numbers that when added together will result in 60. For the first odd number we use X-1 and the second odd number is X-3. We will then add these numbers and equate the result to 60. That is ( X-1) +(X-3) =60 and from this equation we find that X=32. When X =32, one odd number is 32-1= 31 and the other is 32-3=29.

[@major__kong]

Technically, an odd number is represented by 2n + 1. So you have (2n + 1) + (2n + 1 + 2) = 60. Using x works because there are no even solutions. But in more complicated problems you will need to use the proper expression of odd numbers.

[@chanpangchin9744]

The average is 60/2=30 Therefore the numbers are 29,31

[@Vipre-]

Even number so divide by 2 and then add and subtract 1 from that number to get the two consecutive odd integers.

[@tyeadel]

2x + 1 is odd, 2x + 3 is next => 4x + 4 = 60. x = 14 => 2x + 1 = 29 and 2x +3 =31. qed

[@tomtke7351]

immediately one recognizes that two numbers summed = 60 implies each is 30. But they cannot be same and they must be odd and they must be consecutive odd. Seeing the number 30 as a balance point then subtracting one from one number and then adding one the the other yields 29 & 31. These meet all requirements. Furthermore, this is a classic problem requiring two equations in two unknowns. eq.1: N1 + N2 = 60 eq.2: N2 - N1 = 2 ------------------------------------- + : 2N2 = 62 N2 = 31 eq.2: N2 - N1 = 2 31 - N1 = 2 29 = N1

[@henkhu100]

you write: "immediately one recognizes that two numbers summed = 60 implies each is 30" Why? 20 and 40 are also two numbers that "summed = 60", or do you mean "immediately one recognizes that two EQUAL numbers summed = 60 implies each is 30"

[@tomtke7351]

@@henkhu100 the numbers are adjacent... i.e. consecutive odd numbers. They have to be close.

[@henkhu100]

@@tomtke7351 But you write "each is 30. What do you mean by "each"? Which two numbers are 30?

[@budgieboy52]

LET x be an odd number. Thus, the next consecutive odd number is x+2 and so x+×+2=60 2×+2=60 2×=58, subtract 2 from each side X=58/2 ×=29 so x+2=31 39+31=60 QED

[@peterduffy5388]

Did this in my head in 10 seconds

[@tomomalley-df3bq]

5,9,1

[@henryvalero1409]

29 and 31

[@MrMousley]

60 / 2 = 30 ... which is even so the consecutive odd integers are 30 -1 and 30 + 1 29 and 31

[@richardhole8429]

How to do it: read the problem. Realize that the solution must be 30+1 and 30-1. Done.

[@kennethwright870]

60/2 =30, so 29,31

[@bobcornwell403]

I had the answer long before I had the formula. My formula is: n-1 + n + 1 = 60.

[@channelsixtysix066]

29, 31

[@cadfael4598]

I hope this is an elementary school problem because the answer is very obvious. 6/2=30. Odd numbers either side are 29 and 31. Why screw around with algebraic equations?

[@67Pepper]

He's flexing.

[@ez3333]

🌹

[@mohamedathaullah2962]

question should say numbers and not integers as integer is a single digit

[@krunoslavregvar477]

I think there are: 29 and 31

[@sueefo]

29 and 31. Didn’t use algebra.

[@nickclopton7986]

But you are not using algebra which is wat the problem is asking you to do. So if this question was on an algebra test you where to take you would get this question wrong.

[@sueefo]

@@nickclopton7986 So true. Before I watched the rest of the video I did use algebra but I solved it the same way as one of the commentators did.

[@danieldennis9831]

29 and 31

[@petejackson7976]

31 , 29

[@gracieallen8285]

29,31