I need to help my brother with a math question...help?

Question

I'm not sure how to help my brother with these problem:

-Find three consecutive even integers whose sum is 204.
-Find two odd integers whose sum is -76.
-Find three consecutive integers such that sum of the first and third is 62.

I have a clue but I don't know how to explain it to him....

please help :)

Answer 1

1. Divide 204 by 3, we get 68, so the numbers are 67, 68, and 69

2. Any two will do, -50 and -26 or -10 and -66 for example.

3. Divide 62 by 2. We get 31, so they are 30, 31 and 32

Hope this helps

Answer 2

These problems can be solved both algebrically and arithmatically.you dinot specify the manner in which you want to solve these.but as you have used the word integer,i presume you want to solve them algebrically.your first question is to find three consecutive even integers whose sum is 204.let,the integers be x,x+2 and x+4 .Therfore according to the problem, x+x+2+x+4=204 => 3x+6=204 => 3x=204-6=198 =>x=198/6=33.Therefore,the numbers are 33,35 and 37. now,the second problem.This is not a correct problem as the answer may be many i.e.-1and-75, -3 and -73.-5 and -71.-7 and -69, etc. etc.Now,let us proceed to solve the third problem.Let the integers be x,x+1 and x+2.Therefore according to the problem x+x+2=62 =>2x =62-2=60 =>x=60/2=30 .Therefore,the numbers are 30,31 and 32.

Answer 3

1. Consecutive even integers are two apart, like 8 and 10. So set up your variables as x, x + 2 and x + 4. Now add them up.
3x + 6 = 204
3x = 198
x = 66
x + 2 = 68
x + 4 = 70

2. It doesn't specify if you want consecutive integers or not, so there could be lots of answers. -55 + -21 would work. Or -43 + - 33. Lots of possibilities.

3. Consecutive integers are set up as x, x + 1 and x + 2. Add the first and third.
x + x + 2 = 62
2x + 2 = 62
2x = 60
x = 30
x + 1 = 31
x + 2 = 32

The first and third add up to 62

Answer 4

People have solved the first and the last correctly. Most likely the problem wants "CONSECUTIVE odd integers" for the middle one, even though you didn't specifically say that. Since odd numbers are 2 apart, you'd write the equation:
x + x + 2 = -76
2x + 2 = -76
2x = -78
x = -39
-39 + 2 = -37, so the two numbers are -39 and -37.

Answer 5

the answer to the 1st question is 66+68+70
=204
the answer to the second question is -79 + 3
-79+3= -76
the answer to the 3rd question is 30+31+32
30+32=62