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Chapter 3: Q. 350 (page 405)

Find three consecutive even integers whose sum is234.

Short Answer

Expert verified

The sum of three consecutive even integers 76,78,&80is234.

Step by step solution

01

Step 1. Given information    

The sum of three consecutive even integers is234.

02

Step 2. Name the integers

Consider first even integer is n.

second consecutive even integer is n+2.

Third consecutive even integer is n+4.

03

Step 3. Solution

The sum of three consecutive even integers is 234

n+(n+2)+(n+4)=2343n+6=2343n=228n=76

So the first integer isn=76

04

Step 4. Value of consecutive even integers 

Second consecutive even integer

n+2=76+2=78

So Second consecutive even integer is78

Third consecutive even integer

n+4=76+4=80

the third consecutive integer is80

So three consecutive integers arerole="math" localid="1647204442965" 76,78,&80

05

Step 5. Verification 

Sum of 76,78,&80is234

76+78+80=?234234=234

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

Three consecutive even integers are76,78,&80.

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