On one side of a scale there are 6 coins, 3
weighing 2 grams each and 3 weighing x grams
each. The scale is balanced if 5 coins weighing
x grams each are placed on the other side of
the scale.
How much does each of the unknown coins
weigh?
Answer in units of gram
3 grams. If you make the equation
3(2)+3x=5x
then simplify to
6+3x=5x
Then move
6=5x-3x
then simplify
6=2x
then answer
6/2=3
x=3
To solve this problem, we can set up an equation based on the information given.
Let's assume that each unknown coin weighs 'y' grams.
On one side of the scale, we have 6 coins with 3 coins weighing 2 grams each and 3 coins weighing 'y' grams each.
So the total weight on this side of the scale is:
3(2g) + 3(yg) = 6g + 3yg = 6g + 3y grams
On the other side of the scale, we have 5 coins weighing 'y' grams each.
So the total weight on this side of the scale is:
5(yg) = 5y grams
Since the scale is balanced, the weights on both sides should be equal.
So we can set up the equation:
6g + 3y = 5y
Now, we can solve this equation to find the value of 'y'.
6g + 3y = 5y
6g = 5y - 3y
6g = 2y
y = (6g) / 2
y = 3g
Therefore, each of the unknown coins weighs 3 grams.