points] Two alloys A1 and A2 are composed of two basic elements.
The ratios of the compositions of the two basic elements in A1 and A2
are 5 : 3 and 1 : 2, respectively. A new alloy is formed by mixing the
two alloys A1 and A2 in the ratio 4 : 3. What is the ratio of the compo-
sition of the two basic elements in the new alloy?
1:1
To find the ratio of the composition of the two basic elements in the new alloy, we can use the concept of weighted averages.
Let's assume that the two basic elements are X and Y.
1. Determine the total composition of each element in alloys A1 and A2:
- In A1, the composition ratio of X to Y is 5:3. So, if we assume the total composition of A1 as 8 (5+3), then the composition of X would be (5/8) and the composition of Y would be (3/8).
- In A2, the composition ratio of X to Y is 1:2. So, if we assume the total composition of A2 as 3 (1+2), then the composition of X would be (1/3) and the composition of Y would be (2/3).
2. Calculate the weighted average of the compositions of X and Y in the new alloy based on the mixing ratio:
- The mixing ratio of A1 to A2 is given as 4:3. So, if we assume the total composition of the new alloy as 7 (4+3), then the composition of X based on A1 would be (4/7) and the composition of Y based on A2 would be (3/7).
3. Finally, calculate the ratio of the composition of the two basic elements in the new alloy:
The ratio of the composition of X to Y in the new alloy would be (4/7) : (3/7), which simplifies to 4 : 3.
Therefore, the ratio of the composition of the two basic elements in the new alloy is 4:3.