1. ## balancing scales

Imagine the letters(symbols) below to sit on scales.
Scale 1 and 2 are perfectly balanced.

Take D = diamonds H = Heart S = spades.

How many diamonds are needed to balance scale 3?

1. D H ........ S S S S

2. S S D D H ........ H H

3. H S S ........ ?

I get the same answer using both logic and algebra, yet it conflicts with the answer I have been given for this.

2. Hello, aquajam!

Imagine the symbols below to sit on balance scales.

Scales 1 and 2 are perfectly balanced.

. . $\displaystyle [1]\quad\begin{array}{ccccc} \diamondsuit\:\heartsuit && \spadesuit\:\spadesuit\:\spadesuit\:\spadesuit\\ \hline & \Delta \end{array}$

. . $\displaystyle [2]\quad\begin{array}{ccccc} \spadesuit\:\spadesuit\:\diamondsuit\:\diamondsuit \:\heartsuit && \heartsuit\:\heartsuit\ \\ \hline & \Delta \end{array}$

. . $\displaystyle [3]\;\;\begin{array}{ccccc} \heartsuit\:\spadesuit\:\spadesuit && ?\,\diamondsuit \\ \hline & \Delta \end{array}$

How many diamonds are needed to balance [3]

From [1], we have: .$\displaystyle D + H \:=\:4S \quad\Rightarrow\quad H \:=\:4S - D\;\;[4]$

From [2]. we have: .$\displaystyle 2S + 2D + H \:=\:2H \quad\Rightarrow\quad H \:=\:2S + 2D\;\;[5]$

Equate [4] and [5]: .$\displaystyle 4S - D \:=\:2S + 2D \quad\Rightarrow\quad2S \:=\:3D \quad\Rightarrow\quad S \:=\:\tfrac{3}{2}D$

Substitute into [4]: .$\displaystyle H \:=\:4\left(\tfrac{3}{2}D\right) - D \quad\Rightarrow\quad H \:=\:5D$

Substitute into [3]:

. . . . . $\displaystyle H + 2S \;=\;?\,D$

. . $\displaystyle 5D + 2\left(\tfrac{3}{2}D\right) \;=\;?\,D$

. . . . . . . $\displaystyle 8D \;=\;?\,D$

Therefore, 8 Diamonds are needed.

3. 8 is obviously the answer.

4. Yeah I got 8 as well.

The answer given in the book is 3. Must be a misprint.

5. ## Re: balancing scales

Hahahaha aquajam? You're the man

Everybody did get the answer well done.

Yeah I got 8 as well.

The answer given in the book is 3. Must be a misprint.
_________________________________
I love numbers

6. ## Re: balancing scales

Bright minds can easily answer this...:-)

http://treatmentprograms.net/treatme...north-carolina

7. ## Re: balancing scales

If, like some newspaper puzzles I've seen, the force is weight multiplied by distance from the pivot, then the answer is 21, as calculated here.

8. ## Re: balancing scales

Hi

This topic help me a lot in developing my project. I will contribute more when I finished it.

9. ## Re: balancing scales

If you want to get more materials that related to this topic, you can visit:Math teacher interview questions

Best regards.