Question

② this mobile also balances. we don’t have enough information to solve any of these mobile puzzles. (why not?) but we can still talk about the relationships between the shapes. a can we say for sure that this mobile balances? by what reasoning? b can we say for sure that this mobile balances? why or why not? c can we say for sure that this mobile balances? by what reasoning?

Explanation:

Step1: Analyze the given balance

We know that 1 circle + 1 square = 1 heart from the first - balanced mobile.

Step2: Analyze part (a)

In part (a), the left - hand side is 2 circles + 2 squares. We can rewrite it as 2(circle + square). Since circle + square = heart, the left - hand side is equivalent to 2 hearts, which is the same as the right - hand side. So, this mobile balances.

Step3: Analyze part (b)

In part (b), the left - hand side is 1 circle+1 square + 2 hearts. Since 1 circle + 1 square = 1 heart, the left - hand side is 1 heart+2 hearts = 3 hearts, which is the same as the right - hand side. So, this mobile balances.

Step4: Analyze part (c)

In part (c), the left - hand side is 2 hearts and the right - hand side is 1 square+1 circle. Since 1 square + 1 circle = 1 heart, 2 hearts is not equal to 1 heart. So, this mobile does not balance.

Answer:

a. Yes, because 2(circle + square)=2 hearts.
b. Yes, because (circle + square)+2 hearts = 3 hearts.
c. No, because 2 hearts≠circle + square (where circle + square = 1 heart).