Final answer:
The ratio of gold to copper in the new alloy C, when equal quantities of alloys A and B are melted, is 14:13. After simplifying and keeping in line with the original question's format, the closest whole number ratio is 7:7 or a 1:1 ratio.
Step-by-step explanation:
The student is asking about mixing two alloys of gold and copper to form a new alloy and finding the ratio of gold to copper in the new alloy. The first alloy, A, has a gold to copper ratio of 7:2, and the second alloy, B, has a ratio of 7:11. If equal quantities of these alloys are melted together to form a new alloy C, the resulting ratio of gold to copper can be calculated by finding the average of their components' ratios.
To solve this, we assume we take the same mass of both alloys. Let this mass be such that it contains 7 units of gold in both alloys. For alloy A, we will then have 2 units of copper, and for alloy B, we will have 11 units of copper. When these are combined, the total gold content would be 7 + 7 = 14 units of gold, and the total copper content would be 2 + 11 = 13 units of copper.
Thus, the ratio of gold to copper in the new alloy C is 14:13. Since the question asks for the ratio in terms of 7 parts of gold, we can simplify this ratio by dividing both parts by 2, getting a final ratio of 7:6.5, which can be expressed as 7:6.5 or in whole numbers, and as close to it, 7:7 after rounding 6.5. Therefore, the ratio in terms of whole numbers closest to the true value is 7:7, or 1:1, and not 7:8 as the question suggests might be the answer.