Margarit liked to balance things. She balanced 3 pencil sharpeners and 2 one gram blocks witha 100 gram weight and another one gram block. She let x stand for the weight of one pencil sharpener and she claimed that x=30 grams. Was she correct? If not, how much did each pencil sharpener weigh?
NO.
3x = 3 + 100,
x = 103/3 = 34 1/3 Grams.
To solve this problem, let's use algebraic reasoning.
Let's assume that x represents the weight of one pencil sharpener.
Based on the given information, Margarit balanced 3 pencil sharpeners, 2 one-gram blocks, a 100-gram weight, and another one-gram block.
According to her claim, Margarit stated that x = 30 grams for one pencil sharpener.
To determine if Margarit's claim is correct, let's create an equation based on the weights she used:
(3 * x) + (2 * 1g) + 100g + 1g = 0
First, we multiply the weight of each pencil sharpener (x) by the number of pencil sharpeners (3). We then add the weights of the other objects on the balance (2 one-gram blocks, 100-gram weight, and 1-gram block) to the equation.
Simplifying the equation, we have:
3x + 2 + 100 + 1 = 0
3x + 103 = 0
To solve for x, we isolate the variable:
3x = -103
x = -103/3
x ≈ -34.33
From the equation, we find that the weight of one pencil sharpener is approximately -34.33 grams.
Since weight cannot be negative in this context, we can conclude that Margarit's claim is incorrect. The exact weight of each pencil sharpener is not 30 grams.
Therefore, we cannot determine the individual weight of each pencil sharpener without additional information.