Consecutive Integers ! Need help

Question

1) The sum of three consecutive even integers is 390. What are the integers?

 

2) The sum of three consecutive odd integers is 99. What are the integers?

 

3)Which equation defines three consecutive odd integers that add up to 81?

A) n(n+1)(n+2)=81

B) n(n+2)(n+4)=81

C) n+(n+1)+(n+3)=81

D) n+(n+1)+(n+2)=81

E) n+(n+2)+(n+4)=81

 

 

 

 

 

 

 

Answer 1

1) The sum of three consecutive even integers is 390. What are the integers?

 

   In order to ensure the numbers are even I generally call the first

   integer 2n  because 2 multiplied by any number will always be even.

   Our consecutive even integers are:  2n, 2n+2, 2n+4

 

   2n + 2n+2 + 2n+4 = 390

   6n + 6 = 390

   6n = 384

   n = 64

 

  Our 1st integer is 2n = 2(64) = 128

  Our integers are 128, 130, 132

 

Check:  128+130+132 = 390 which is correct.

 

2) The sum of three consecutive odd integers is 99. What are the integers?

 

    Same logic applies:  An odd integer will always result from 2n+1

    So we will call our 3 consecutive odd integers   2n+1, 2n+3, 2n+5

 

   2n+1 + 2n+3 + 2n+5 = 99

   6n+9 = 99

   6n = 90

   n = 15

   Our first odd integer is 2n+1 = 2(15) + 1 = 31

   Our 3 consecutive odd integers are 31, 33, 35

 

Check:  31 +33+45 = 99  Yes

 

3)Which equation defines three consecutive odd integers that add up to 81?
A) n(n+1)(n+2)=81
B) n(n+2)(n+4)=81
C) n+(n+1)+(n+3)=81
D) n+(n+1)+(n+2)=81
E) n+(n+2)+(n+4)=81

 

We can immediately discard answers A, B because they are multiplying

instead of adding.

That leaves C, D, E

 

This question does not follow the logic I utilized in question 1 and 2. 

Assuming the first number is indeed odd and is called n

The next odd number is n+2 followed by n+4

Thus we must have:  n + (n+2) + (n+4) = 81

The answer is E

 

By the way:  The numbers are 25, 27, 29