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Three consecutive integers add up to 51. What are these integers?
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Three consecutive integers add up to 51. What are these integers?
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Answer:
let the numbers be a-d ,a ,a+d
By given condition
a-d+a+a+d=51
3a =51
a=51/3
a=17
Given : The sum of three consecutive integers is 51.
To find : The consecutive integers.
[tex]\\[/tex]
[tex]\qquad[/tex]_______________
[tex]\\[/tex]
According to the question, let :
[tex]\qquad[/tex] ❍ First integer = [tex]\sf x[/tex]
[tex]\qquad[/tex] ❍ Second integer = [tex]\sf x+1[/tex]
[tex]\qquad[/tex] ❍ Third integer = [tex]\sf x+2[/tex]
We are given that their results 51, so we get an equation as follows :
[tex] \sf \qquad \dashrightarrow \: x + (x + 1) + (x + 2) = 51[/tex]
[tex] \sf \qquad \dashrightarrow \: x + x + x + 1 + 2 = 51[/tex]
[tex] \sf \qquad \dashrightarrow \: 3x + 3 = 51[/tex]
[tex] \sf \qquad \dashrightarrow \: 3x = 51 - 3[/tex]
[tex] \sf \qquad \dashrightarrow \: 3x = 48[/tex]
[tex] \sf \qquad \dashrightarrow \: x = \cancel{\dfrac{48}{3} }[/tex]
[tex] \sf\qquad \dashrightarrow \: x = 16[/tex]
So, the number is 16.
[tex]\\[/tex]
[tex]\qquad[/tex]_______________
[tex]\\[/tex]
Finding the numbers :
We shall find the numbers by substituting them :
[tex]\qquad[/tex]❍ First number : x = 16
[tex]\qquad[/tex]❍ Second number : x+1 = 17
[tex]\qquad[/tex]❍ Third number : x+2 = 18