The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers.

Answer 1

First, we need to write two consecutive integers. Call the smaller integer x. Then the larger integer is x+1. One less than three times the smaller integer is 3x-1, which is the sum of the two:

x + (x+1) = 3x-1

2x+1=3x-1

Solve for x to get x=2.The two integers are 2&3.

Indeed, 5 is one less than three times two.

I hope this helps!

Have fun mathing,

Liz Z.

Answer 2

If x is the 1st (smaller) integer, then x + 1 is the larger integer.

The sum is x + (x + 1), or 2x + 1

Three times the smaller is 3x.

The sum is one less than three times the smaller: (2x + 1) = 3x - 1

x = 2; x + 1 = 3

Check: One less than three times the smaller = 3(2) - 1 = 5

Sum = 2 + 3 = 5

Answer 3

Hi Samari! The key to solving a problem like this is to translate the english sentence in to an equation. To begin with, I'll replace "is" with an equal sign:

"The sum of two consecutive integers" = "one less than three times the smaller integer"

Now, we need to denote our unknown numbers by variables. Call the smaller one x, and the larger one x + 1 (because the numbers are consecutive). Can you translate the two english sentence to be expressed in terms of x?