SOLUTION: If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers?      Log On


   

Question 85432: If one-half of a number is added to one-third of the next consecutive number, the sum is 67. What are the two numbers?
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
x = "a number"
x + 1 = next consecutive number
1%2F2x + 1%2F3(x + 1) = 67
Multiply by the LCD which is 6:
(6)1%2F2x + (6)1%2F3(x + 1) = 6(67)
Simplify:
3x + 2(x + 1) = 402 [the idea was to eliminate the fractions]
Distributive property:
3x + 2x + 2 = 402
Combine like terms:
5x + 2 = 402
Subtract 2 from both sides:
5x = 400
Divide both sides by 5:
x = 80
x + 1 = 80 + 1 = 81
The two numbers are 80 and 81