A balance scale is perfectly balanced with two blocks on one side and ten weights on the other. If each weight equals 2.0 grams, how much does one block weigh?
Please answer and explain.
To find out how much one block weighs, we need to use algebra to solve the problem. Let's breakdown the information given:
1. Two blocks are on one side of the scale.
2. Ten weights are on the other side.
3. Each weight equals 2.0 grams.
Let's denote the weight of one block as "x" grams.
On one side of the balance scale, we have 2 blocks, so their combined weight would be 2x grams.
On the other side of the scale, we have 10 weights, and each weight weighs 2.0 grams. So the combined weight of the 10 weights is 10 * 2.0 = 20 grams.
Since the scale is perfectly balanced, the weight on one side should equal the weight on the other side.
Therefore, we have the equation:
2x = 20
To find the weight of one block, we need to solve the equation for "x". Let's do that:
Divide both sides of the equation by 2:
2x/2 = 20/2
x = 10
Therefore, one block weighs 10 grams.