Respuesta :
Answer: The integers are 52,53,54.
Step-by-step explanation:
Let the three consecutive integers are
[tex]x,x+1,x+2[/tex]
Since we have given that
The sum of the first two is 51 more than the third,
According to question,
[tex](x+x+1)-(x+2)=51\\\\2x+1-x-2=51\\\\x-1=51\\\\x=51+1\\\\x=52[/tex]
So, the three consecutive integers are
52,52+1,52+2
52,53,54.
Hence, the integers are 52,53,54.
The consecutive integers are [tex]\boxed{52}, \boxed{53}[/tex] and [tex]\boxed{54}[/tex] if the sum of two is 51 more than the third.
Further explanation:
The numbers that have a difference of 1 between every next number is known as the consecutive
Explanation:
The sum of the first two is 51 more than the third.
Consider the first number of consecutive integers as [tex]\text{p}[/tex].
So the second number of consecutive integers is [tex]\text{p}+1.[/tex]
Therefore, the third number of consecutive integers is [tex]\text{P}+2[/tex]
The sum of first two numbers is 51 more than the third.
[tex]\begin{aligned}\left( x \right) + \left( {x + 1} \right) &= 51 + \left( {x + 2} \right)\\x + x + 1 &= 51 + x + 2\\2x + 1 &= 53 + x \\2x - x &= 53 - 1\\x&= 52\\\end{aligned}[/tex]
The first number of consecutive integers is 52.
The second number of consecutive integer can be obtained as follows,
[tex]\begin{aligned}{\text{Second integer}} &= p + 1\\&= 52 + 1\\&= 53\\\end{aligned}[/tex]
The third number of consecutive integer can be obtained as follows,
[tex]\begin{aligned}{\text{Third integer}} &= p + 2\\&= 52 + 2\\&= 54\\\end{aligned}[/tex]
The consecutive integers are [tex]\boxed{52}, \boxed{53}[/tex] and [tex]\boxed{54}[/tex] if the sum of two is 51 more than the third.
Learn more
- Learn more about the polynomial https://brainly.com/question/12996944
- Learn more about logarithm model https://brainly.com/question/13005829
- Learn more about the product of binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: consecutive, three consecutive, sum, addition, integers, more, 51 more, consecutive integers, first two.
