John weighs twice as much as Marcia. Marcia is 60 percent of Bob's weight. Dave weighs 50 percent of Lea's weight. Lea weighs 190 percent of John's weight. What is Bob's weight?

Answer 1

To solve this, first write the statements as equations. For simplicity, let's just use the first letter of each person's name (e.g. 'J' is for John):

J = 2M

M = 0.60B

D = 0.50L

L = 1.9J

The next step is a little tricky, but it essentially consists of taking one of the equations and substituting the values of the known variables. For example, instead of writing J = 2M, you can use the equation M = 0.60B to substitute in this known value for M. This would give you J = 2(0.60B).

Showing this substitution step-by-step:

D = 0.50L

D = (0.50)(1.9J)

D = (0.50)(1.9)(2M)

D = (0.50)(1.9)(2)(0.60B)

D = 1.14B

This means that Dave weighs 1.14 times (or 114% more than) the weight of Bob.

Rewrite this with 'B' alone on one side of the equation:

B = D/1.14

B = D(1/1.14)

B = D(0.87)

And this means that Bob weighs about 87 percent of Dave's weight.

Answer 2

Bob's weight cannot be determined from the information given. There are five unknown weights but only four linear equations.