Final answer:
The density of metal A is 2 g/cm³, derived from simultaneous equations based on the given masses of the metals and the total volume of the alloy.
Step-by-step explanation:
To find the density of metal A, we need to use the given information about the alloy comprised of metals A and B, their masses, and the alloy's total volume. The alloy is a mixture of 24 g of metal A and 30 g of metal B with a total volume of 6 cm3. Let's denote the density of metal A as dA (g/cm3).
Given that the density of metal B (dB) is 2 g/cm3 greater than that of metal A, we can express the density of metal B as dA + 2 g/cm3. Now, we can write the equations for the mass of each metal based on the density formula, which is mass = density × volume. Since we don't know the individual volumes of metals A and B, we'll let the volume of metal A be VA and the volume of metal B be 6 cm3 - VA (since the total volume is 6 cm3).
The mass of metal A is therefore 24 = dA × VA and the mass of metal B is 30 = (dA + 2) × (6 - VA). We now have two equations and two unknowns (dA and VA), which we can solve simultaneously. After solving, we get the density of metal A as 2 g/cm3.