Mass box A=10grams Mass box B=5 grams; Mass box C -made of one A and one B How many grams of A would be needed to give the same number of particles: : as 7.5 grams of B? square i as 2.5 grams? square as 12.5 grams? square as 1 gram? square

To solve this problem, we need to understand the relationship between the masses of boxes A and B and how they relate to the number of particles.<br /><br />Given:<br />- Mass of box A = 10 grams<br />- Mass of box B = 5 grams<br /><br />We assume that the number of particles is directly proportional to the mass. Therefore, if you have a certain mass of B, you can find the equivalent mass of A that contains the same number of particles by setting up a proportion.<br /><br />1. **As 7.5 grams of B:**<br /><br /> Since 5 grams of B is equivalent to 10 grams of A (because one B is half the mass of one A), we set up the proportion:<br /><br /> \[<br /> \frac{5 \text{ grams of B}}{10 \text{ grams of A}} = \frac{7.5 \text{ grams of B}}{x \text{ grams of A}}<br /> \]<br /><br /> Solving for \( x \):<br /><br /> \[<br /> x = \frac{7.5 \times 10}{5} = 15 \text{ grams of A}<br /> \]<br /><br />2. **As 2.5 grams of B:**<br /><br /> Using the same method:<br /><br /> \[<br /> \frac{5 \text{ grams of B}}{10 \text{ grams of A}} = \frac{2.5 \text{ grams of B}}{x \text{ grams of A}}<br /> \]<br /><br /> Solving for \( x \):<br /><br /> \[<br /> x = \frac{2.5 \times 10}{5} = 5 \text{ grams of A}<br /> \]<br /><br />3. **As 12.5 grams of B:**<br /><br /> Again, using the proportion:<br /><br /> \[<br /> \frac{5 \text{ grams of B}}{10 \text{ grams of A}} = \frac{12.5 \text{ grams of B}}{x \text{ grams of A}}<br /> \]<br /><br /> Solving for \( x \):<br /><br /> \[<br /> x = \frac{12.5 \times 10}{5} = 25 \text{ grams of A}<br /> \]<br /><br />4. **As 1 gram of B:**<br /><br /> Finally, for 1 gram of B:<br /><br /> \[<br /> \frac{5 \text{ grams of B}}{10 \text{ grams of A}} = \frac{1 \text{ gram of B}}{x \text{ grams of A}}<br /> \]<br /><br /> Solving for \( x \):<br /><br /> \[<br /> x = \frac{1 \times 10}{5} = 2 \text{ grams of A}<br /> \]<br /><br />Therefore, the answers are:<br />- As 7.5 grams of B: 15 grams of A<br />- As 2.5 grams of B: 5 grams of A<br />- As 12.5 grams of B: 25 grams of A<br />- As 1 gram of B: 2 grams of A