Question

On one side of a balancing scale there are 5 blocks: 3 weighing 3 grams each and 2 weighing x each. The scale is balanced if 8 blocks weighing x grams each are placed on the other side of the scale. How many does each side of the unknown blocks weigh

Answer 1

The weight of unknown block on each side of the scale is 1.5 grams.

Explanation:

The number of blocks on 1 side = 5 blocks

Now, 3 blocks = 3 grams each

⇒Total weight of 3 blocks = (3 grams )times 3 = 9 grams

2 blocks = x grams each

⇒Total weight of 2 blocks = (x grams ) 2 = 2 x grams

So the total weight on 1 side = weight of 5 blocks combined

= 9 grams + 2x grams = (9 + 2x) grams

The total weight on other side of scale = 8 blocks times (x grams)

= (8x) grams

Now, The SCALE IS BALANCED if :

(9 + 2x) grams = (8x) grams

or, 9 + 2x = 8x

⇒9 = 8x - 2x = 6x

or, x = 9/6 = 1.5

⇒ x = 1.5 grams

Hence, the weight of unknown block on each side of the scale is

1.5 grams, so that the scale is balanced.