After losing 28 pounds, an individual weighs 98 pounds more than one-third his previous weight. Find the previous weight of the individual

Answer 1

First, define the variables. Let's let W be "the previous weight of the individual" since that is what we are looking for.

If the person loses 28 pounds then their new weight is W - 28. The problem says that their new weight is 98 pounds more than 1/3 their previous weight. 1/3 their previous weight is 1/3W. 98 pounds more than one-third his previous weight is 98 + 1/3W

So W - 28 = 98 + 1/3W

To solve, first add 28 to both sides of the equation

W - 28 = 98 + 1/3W

+28 +28

---------------------------

W = 126 + 1/3W

Now, subtract 1/3W from both sides:

W = 126 + 1/3W

-1/3W -1/3W

2/3W = 126

Now, multiply both sides by the reciprocal of 2/3 (which is 3/2)

2/3W = 126

x3/2 x3/2

W = 189 pounds

Let's double check:

If he loses 28 pounds, he would be 189 - 28 = 161

1/3 of his original 189 pounds is 63 pounds and 98 pounds more than that is 161 as well. We did it!

Answer 2

x - 28 = 98 + (1/3)(x)

(2/3)(x) = 126

2x = 378

x = 189 is the previous weight of the individual