Solve: Find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number?

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emileefoley emileefoley · Answer 1 · 2018-11-06T21:50:19+01:00

Answer: 8

Step-by-step explanation: 6,7,8 are the consecutive integers because 6+7(2)=20

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rejkjavik rejkjavik · Answer 2 · 2018-11-06T21:55:08+01:00

We are given

Let's assume

smallest even integer =x

Since, each even integers are difference of 2

so, middle term =x+2

so, largest term =x+2+2=x+4

the sum of the smallest number and twice the middle number is 20 more than the largest number

so, we get

[tex]x+2(x+2)=20+x+4[/tex]

now, we can solve for x

[tex]x+2x+4=20+x+4[/tex]

[tex]x+2x+4=x+24[/tex]

[tex]3x+4=x+24[/tex]

[tex]2x=20[/tex]

Divide both sides by 2

[tex]x=10[/tex]

so, smallest even integer=10

middle even integer=12

largest even integer=14............Answer