Question

After losing 30 pounds, an individual weigh 110 pound more than one-third his previous weight

Answer 1

Write an equation based on the problem
For an instance, x is the previous weight
"After losing 30 pounds" could be written as (x - 30)
"110 pounds more than one-third his previous" could be written as (110 + $\frac{1}{3}$x)

Join the expression and solve for x
x - 30 = 110 + $\frac{1}{3}$x

Move 1/3 x to the left side, and the constant of 30 to the right side, so like terms will be on equal side
x - $\frac{1}{3}$x = 110 + 30

Equalize the denominators of the fractions
$\frac{3}{3}$x - $\frac{1}{3}$x = 140
$\frac{2}{3}$ = 140
x = 140 × $\frac{3}{2}$
x = 420/2
x = 210

The previous weight was 210 pounds
The new weight is 210 - 30 = 180 pounds