ODD, EVEN, & ODD, EVEN, & CONSECUTIVE CONSECUTIVE

INTEGERSINTEGERS

The sum of 2 The sum of 2 consecutive consecutive integers is integers is 63. Find the 63. Find the numbers.numbers.

SOLUTION: Let x =be the first integerSOLUTION: Let x =be the first integer then x+1 = the 2then x+1 = the 2ndnd integer integerThe sum is 63:The sum is 63:

x+x+1=63 x+x+1=63 2x+1=632x+1=63

2x=63-12x=63-1 2X=622X=62

x=31x=31 x+1=32x+1=32

So 31 and 32 are the numbers. So 31 and 32 are the numbers. Proof: 31+32=63Proof: 31+32=63

The sum of 3 consecutive The sum of 3 consecutive odd integers is 75. Findodd integers is 75. Find

the the consecutive odd consecutive odd integers.integers.

SOLUTION: Let x =be the first integerSOLUTION: Let x =be the first integer x+2= the 2x+2= the 2ndnd integer integer

x+4= the 3x+4= the 3rdrd integer integerThe sum is 75.The sum is 75.

x+x+2+x+4=75x+x+2+x+4=75 3x+6=753x+6=75

3x=75-63x=75-6 3x=693x=69

x=23x=23 x+2=25x+2=25

x+4=27x+4=27So the numbers are 23, 25 and 27.So the numbers are 23, 25 and 27.

Proof: 23+25+27=75Proof: 23+25+27=75

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