# A clown weighs 60 lb more than a trapeze artist. The trapeze artist weighs two thirds as much as the clown. How much does each weigh?

Jan 6, 2017

Oh, a fun word problem.

#### Explanation:

Okay.

Let C be the clown, and T be the trapeze artist.

We can form these equations:

(1) C = T + 60 lbs
(60 lbs more than the trapeze artist), and

(2) T = 2/3 * C
(only 2/3 as much as the clown),

giving us a system of two equations in two variables.

Let's take the expression for the Clown, T + 60, and substitute it in for C in the other equation:

T = 2/3*( T + 60)

giving us

T = (2/3)T + (2/3)(60) [subtract (2/3)*T from both sides] =>

T - (2/3)T = (2*60)/ 3 =>

T/3 = 120/3 =>

T/3 = 40 =>

T = 40*3 =>

T = 120,
which means that the Clown weighs

T + 60, or 120 + 60 = 180.

So, the Clown weighs 180 lbs and
the Trapeze artist weighs 120 lbs.

Let's see if this is correct.

Our two equations are:

(1) C = T + 60 lbs
and
(2) T = 2/3 * C

180 does = 120 + 60, and
120 does = 2/3 times 180.

[One-third of 180 is 60, and 60 times 2 is 120.]