Question 85432
x = "a number"
x + 1 = next consecutive number

{{{1/2}}}x + {{{1/3}}}(x + 1) = 67

Multiply by the LCD which is 6:

(6){{{1/2}}}x + (6){{{1/3}}}(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