Question

The sum of three consecutive integers is 12 more than twice the largest of the integers. Find all integers

Answer 1

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Let the 3 consecutive integers be a, a+1, and a+2.

The sum of these integers equates to a + a+1 + a+2.

....is (equals to) 12 more (means add 12) than twice (2 times) the largest integer (a+2).

Now put everything together

a + a+1 + a+2 = 12 + 2(a+2)

Let’s solve for a

3a + 3 = 12 + 2a + 4

3a + 3 = 16 + 2a

3a - 2a = 16 - 3

a = 13

first integer = a = 13

second integer = a+1 = 14

third integer = a+2 = 15

To confirm, let’s plug in the above numbers into the following equation to see if they equal each other.

a + a + 1 + a + 2 = 12 + 2(a+2)

13 + 14 + 15 = 12 + 2(15)

42 = 12 + 30

42 = 42!