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?
1 Answer
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.]
