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Chapter 3: Q. 351 (page 405)

Find three consecutive odd integers whose sum is51.

Short Answer

Expert verified

The sum of three consecutive odd integers 15,17,&19is51.

Step by step solution

01

Step 1. Given information    

The sum of three consecutive odd integers is 51

02

Step 2. Name the integers 

Consider first odd integer is n

The second consecutive odd integer is n+2

The third consecutive odd integer is n+4

03

Step 3. Solution 

The sum of three consecutive odd integers is51

n+(n+2)+(n+4)=513n+6=513n=45n=15

So the first odd integer isn=15

04

Step 4. Value of consecutive odd integers  

A second consecutive odd integer

n+2=15+2=17

So Second consecutive odd integer is 17

Third consecutive even integer

n+4=15+4=19

the third consecutive odd integer is 19

So three consecutive odd integers are15,17,&19

05

Step 5. Verification 

Sum of 15,17,&19is 51

15+17+19=?5151=51

The left-hand side is equal to the right-hand side, so our answer is correct

Three consecutive odd integers are 15,17,&19

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