The sum of three consecutive integers is 18 more than 2 times the largest number. Find the three numbers.

Answer 1

Hi Pricila L.

19, 20, and 21

You have 3 consective numbers

x

x+1

x+2

Their sum is equal to 18 more than twice the largest number

18 + 2(x+2)

Therefore

x + x +1 + x + 2 = 18 + 2(x + 2)

Combine like terms

3x + 3 = 18 + 2x + 4

3x + 3 = 22 + 2x

Isolate the variables and constant on opposite sides of the equal sign by

Subtractig 2x from both sides of the equation and subtracting 3 from both sides of the equation

3x - 2x = 22 - 3

x = 19

Make the substitutions in the original equations

x+1 = 20

x+2= 21

18 +2(x+2) = 18 + 2(21) = 18 + 42

Repeat with the numbers

19 + 20 + 21 = 18 + 42

60 = 60

Hope this helps