A clown weighs 60lb more than a trapeze artists. The trapeze artist weighs two thirds as much as the clown. How much does each weigh? Choices for the weight of the trapeze artist: 110,120,125
trapeze artist --- x
clown --------- x + 60
x = (2/3)(x+60)
x = (2/3)x + 40
(1/3)x = 40
x = 120
trapeze artist weighs 120 lbs
clown weighs 180 lbs
Let's denote the weight of the trapeze artist as x.
According to the problem, the clown weighs 60 pounds more than the trapeze artist. Therefore, the weight of the clown can be represented as (x + 60).
The problem also states that the trapeze artist weighs two-thirds as much as the clown. This can be written as:
x = (2/3) * (x + 60)
To solve for x, we can start by simplifying the equation:
3x = 2(x + 60)
Distributing 2:
3x = 2x + 120
Subtracting 2x from both sides:
x = 120
Therefore, the weight of the trapeze artist is 120 pounds.
Now, we can find the weight of the clown:
Weight of the clown = x + 60 = 120 + 60 = 180 pounds.
So, the weights are:
Trapeze artist: 120 pounds
Clown: 180 pounds
None of the given choices (110, 120, 125) matches the result we obtained.
To solve this problem, let's assign variables to represent the weights of the trapeze artist and the clown. Let's say the weight of the trapeze artist is represented by 'T', and the weight of the clown is represented by 'C'.
According to the given information, the clown weighs 60 pounds more than the trapeze artist, which can be expressed as:
C = T + 60
Also, it is mentioned that the trapeze artist weighs two-thirds of the clown. In mathematical terms, this can be expressed as:
T = (2/3)C
Now we have a system of two equations:
C = T + 60
T = (2/3)C
To find the weights of the trapeze artist and the clown, we can solve this system of equations. Substituting the value of T from the second equation into the first equation, we get:
C = (2/3)C + 60
To solve for C, we'll eliminate the fraction by multiplying both sides of the equation by 3:
3C = 2C + 180
Next, we'll subtract 2C from both sides of the equation:
C = 180
Therefore, the weight of the clown is 180 pounds.
To find the weight of the trapeze artist, we can substitute this value of C back into one of the original equations:
T = (2/3)C
T = (2/3)(180)
T = 120
Therefore, the weight of the trapeze artist is 120 pounds.
Therefore, the correct answer from the given choices is 120.