Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417.Let n be the first one. Write an equation that will determine the three integers.
let the middle number be n
let the smallest be n-1
let the largerst be n+1
then
(n-1)+(n)+(n+1) = 417
3n = 417
n = 139
the numbers are 138, 139 and 140
or
let the smallest be x
the middle one be x+1
and the largest x+2
then x + x+1 + x+2 = 417
3x + 3 = 417
3x = 414
x = 138
notice now we found the first number, since we defined it that way, the other two are 139 and 140
Does the first method look easier?
yes thankyou
Well, using the information given, we can form the equation as follows:
n + (n+1) + (n+2) = 417
That's three consecutive integers: n, n+1, and n+2. And their sum is 417.
To find the three consecutive integers, we can assign a variable to the first integer and then express the other two integers in terms of that variable.
Let n be the first integer. The second consecutive integer would be n + 1, and the third consecutive integer would be n + 2.
Now, let's add up these three integers and set it equal to 417:
n + (n + 1) + (n + 2) = 417
Simplifying this equation, we get:
3n + 3 = 417
To solve for n, we can subtract 3 from both sides of the equation:
3n = 417 - 3
3n = 414
Finally, we divide both sides of the equation by 3:
n = 414 / 3
n = 138
So, the first consecutive integer is 138. The second consecutive integer is 138 + 1 = 139, and the third consecutive integer is 138 + 2 = 140.