Chapter 1.7, Problem 6P

To determine

To calculate: Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given.A clown weighs 60 lb. more than a trapezium artist. 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

Answer to Problem 6P

weight of the artist $a=120$ and weight of the clown $a+60=120+60=180$ .

Explanation of Solution

Given information:A clown weighs 60 lb more than a trapezium artist and the trapeze artist weighs two thirds as much as the clown.

Calculation:

Step 1: Here we have two unknowns.

Step 2: Let $a$ be the weight of trapeze artist, so that $a+60$ is weight of clown.

Step 3: As given, the trapeze artist weighs two thirds as much as the clown such that

  $a=\frac{2}{3}\left(a+60\right)$ .

Step 4: Choices for $a$ are given as 110, 120, 125

$a$	$a=\frac{2}{3}\left(a+60\right)$	True / False
110	$110=\frac{2}{3}\left(110+60\right)$	False
120	$110=\frac{2}{3}\left(120+60\right)$	True
130	$110=\frac{2}{3}\left(130+60\right)$	False

From above table we can say that weight of the artist $a=120$ and weight of the clown

  $a+60=120+60=180$

Step 5: Now we verify the answer

The weight of clown is 60 pounds more than the trapeze artist: $180=120+60$ , which is correct

The trapeze artist weighs two thirds of the clown: $\frac{2}{3}\left(180\right)=120$ , which is also correct.