Question

lesson 8
reasoning about solving equations (part 2)

1. i can explain how a balanced hanger and an equation represent the same situation.
2. i can explain why some balanced hangers can be described by two different equations, one with parentheses and one without.
3. i can find an unknown weight on a hanger diagram and solve an equation that represents the diagram.
4. i can write an equation that describes the weights on a balanced hanger.

write an equation to represent the hanger diagram. solve and explain your reasonin
hanger diagram with three triangular weights labeled a and three rectangular weights labeled a on one side, and a rectangular weight labeled 18 on the other side

Explanation:

Step1: Count the number of \( a \)

On the left side of the hanger, we have 3 triangular weights (each \( a \)) and 3 rectangular weights (each \( a \)), so total number of \( a \) is \( 3 + 3=6 \). On the right side, we have a weight of 18. So the equation is \( 6a = 18 \).

Step2: Solve for \( a \)

To solve \( 6a = 18 \), we divide both sides by 6. So \( a=\frac{18}{6}=3 \).

Answer:

The equation is \( 6a = 18 \) and the solution is \( a = 3 \).