Answer to Question #1592 in Algebra for Hannah

Question

How do you solve this problem?

Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 18 more than three times the largest number.
______ (smallest value)
______ (largest value)

Answer 1

Denote these three numbers as x, x+1 and x+2.
The twice sum of two smallest numbers would be 2(x+(x+1)) = 18 + 3(x+2).
Let's find the x:
2x+2x+2 = 18 + 3x + 6
x = 22
x+1 = 23
x+2 = 24
smallest value is 22;
the largest value is 24