Question

Can you please help with questions 1&2. As they go together. Directions are with the pic below.

Answer 1

Given: Three balances A, B, and C

To Determine: Which block will balance C

Solution

Let a be number of sphere, b be the number of cylinder, and c the number of cube

So

`\begin{gathered} BalanceA:2a+b+c=a+3b \\ BalanceB:3b=2c \\ BalanceC:a+2c=b+c \end{gathered}`
`\begin{gathered} 2a+b+c=a+3b \\ 2a-a+b+c=3b \\ a+b+c=3b \\ Note \\ 3b=2c \\ Therefore \\ a+b+c=2c \\ 2c=a+b+c===compare\text{ with Balance C} \\ a+2c=b+c \\ a+2c=a+a+b+c \\ a+2c=2a+b+c \end{gathered}`

Hence, 2 spheres will balance C

I figured this out by what will balance one of side of by combining balance A and balance B