A sheet of stone paper is made from calcium carbonate and resin in the ratio 4 : 1 by mass. One sheet weighs 960 grams. How much calcium carbonate does it contain?

Step-by-step solution

1. 1

   Turn the ratio into a count of equal parts. A ratio of $4:1$ means the sheet can be cut into $4$ identical parts of calcium carbonate plus $1$ identical part of resin. The key move is adding the ratio numbers to find how many parts make the whole:

   $4+1=5\ \text{parts}$

2. 2

   Find the mass of one part. All five parts are the same size, so divide the total mass by the number of parts:

   $960\div 5=192\ \text{g per part}$

   This single number is what makes ratio problems easy — every share is a whole-number multiple of it.

3. 3

   Scale up to the share you were asked for. Calcium carbonate is $4$ parts:

   $4\times 192=768\ \text{g}$

   $\boxed{768\ \text{g}}$

4. 4

   Check that the shares rebuild the total. Resin is $1$ part, or $192$ g, and

   $768+192=960\ \text{g}$

   which is the original mass, so nothing was lost or double-counted. The ratio also checks out: $768:192=4:1$.

5. 5

   Express it in other units if the question asks. Since $1$ kg $=1000$ g,

   $768\ \text{g}=0.768\ \text{kg}$

   and as a fraction of the sheet the calcium carbonate is $\tfrac{4}{5}=80\%$ of the mass.