Question

A balanced scale has 3 marbles, 2 pennies, and 4 quarters on one side and 4 marbles, 2

quarters, and 1 penny on the other side. If pennies weigh one gram and quarters weigh
3 grams, find the weight of a marble. Explain or show your reasoning.

Answer 1

See image

Explanation:

An equation is really like a scale with two equal things on both sides. You could use the idea of a scale and lift off the same amount from both sides to keep it balanced. But I will show you the algebra version. When we subtract the same thing from both sides that's how we work back to our answer while keeping the scale balanced.

Let m = weight of a marble

p = weight of a penny = 1 gram

q = weight of a quarter= 3 grams

The problem says how many of each marble, penny, quarter, then set them equal to each other. See image