when the smaller of two even consecutive integers is added to three times the larger the result is 230?

Question

find the smaller integer

Answer 1

x+ 3(x+2)= 230
x=56

Answer 2

Enough people have solved this problem. I just want to point out the value of rereading your word problem after you are done.

For example some solutions used x and x+2 which may also be two consecutive odd numbers. Some problems have many answers, so an odd answer would have fit the equation, but not answered the problem.

Also, in English, problems may have similar wording but mean exactly the opposite thing.

If you make a habit of checking that your answers solve the problem, you won't have to nail the formula exactly right on the first try.

Coming up with the wrong formula is a part of mathematics. Sometimes it takes centuries to solve a problem, or learn it can't be solved. But someone has to start guessing at a solution to get the ball rolling.

Consider Fermat's Last Theorem. Fermat thought he had an answer, but if he did, no one ever found it, so his answer was probably flawed. Or maybe he just had a sadistic sense of humor. If so, his prank fooled a lot of mathematicians for a long time.

Once you learn how to check your answers. You can experiment with different formulas. Often these formulas can be corrected.

Another way to get the answer is trial and error. (Though your teacher may not always approve.)

Testing a few numbers may let you see the pattern to solve the formula.

Although I could not help you with this problem, I hope I've put a few more tools in your math toolbox.

I think that it is very important to realize that mathematics is a lot like writing. A lot of editing has gone on to the examples that finally appear in a book. Many students do not realize that math rarely is as cut and dry as this, and feel frustrated, and even stupid when answers don't jump out at them.

Well the answers are not always obvious, even when the books write them that way.

Answer 3

rewrite the question in math symbols:

two even consecutive integers: x and x + 2

three times the larger: 3*(x+2)

add the smaller to three times the larger:

x + 3*(x+2) = 230

x + 3x + 6 = 230

4x + 6 = 230

4x = 224

x = 56

Answer 4

x = smaller integer
(x + 2) = larger integer; both are even and consecutive, thus the difference is 2

x + 3(x + 2) = 230
x + 3x + 6 = 230
4x + 6 = 230
4x = 224
x = 56

The smaller integer is 56

Answer 5

Any even number can be denoted by 2k where k is an any integer.
If 2k is smaller, 2k+2 is larger even number which are consecutive integers.
Three times the larger is equal to 3*(2k+2) = 6k+6
The smaller is 2k

The addition of these terms
6k+6+2k = 8k+6 = 230 => 8k = 224 => k= 28

The smaller is 2k= 56.
The bigger is 2k+2= 58

Check: 56 + 3 * 58 = 230

Answer 6

there seems to be a lot of algebra 2 going on here today

I hope you students are learning something and not just getting somebody else to do your homework so you can more easily fail the tests.

s = smaller number
s+2 = equals larger number (see how the plus 2 makes them either even or odd consecutive numbers)

now we write algebra that is the same as the words in the problem statement - smaller added to 3 times larger equals 230

s+3(s+2) = 230

or s+3s +6 =230

4s+6 = 224

4s=224

s=56 got it? wasn't that fun?

Answer 7

56

Answer 8

56

Answer 9

smaller integer: x
larger integer: x+2

x+3(x+2)=230
x+3x+6=230
4x=224
x=56

Answer 10

the smaller number is 56 while the larger number is 58