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

Answer:

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

Step-by-step 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.