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Three consecutive integers are as such they are taken in increasing order and multiplied by 2, 3, and 4, respectively, they add up to 56. Find these numbers.
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Three consecutive integers are as such they are taken in increasing order and multiplied by 2, 3, and 4, respectively, they add up to 56. Find these numbers.
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Answer:
It is given that the three consecutive integers multiplied by 2, 3, and 4 respectively, add up to 74. Therefore, the smallest consecutive integer out of the three numbers is 7. Therefore, the three consecutive integers are 7, 8, and 9.
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[tex]Let \: 3 \: Consecutive \: integers \\ : x , \: x+1 \: , \: x+2 [/tex]
[tex]As \: per \: Question [/tex]
[tex]2x + 3(x + 1) + 4(x + 2) = 56[/tex]
[tex]2x + 3x + 3 + 4x + 8 = 56[/tex]
[tex]9x + 11 = 56[/tex]
[tex]9x = 56 - 11[/tex]
[tex]9x = 45[/tex]
[tex]x = \frac{45}{9} [/tex]
[tex]x = 5[/tex]
[tex]x + 1 = 5 + 1 = 6[/tex]
[tex]x + 2 = 5 + 2 = 7[/tex]
[tex]Number \: are \: \: 5 , 6 \: and \: 7 [/tex]