Final answer:
Brady can divide his 36 trophies into two groups that maintain a 4:5 ratio by placing 16 trophies in the first group and 20 trophies in the second group.
Step-by-step explanation:
The student's question involves dealing with the division of trophies into two groups so that they keep a certain ratio, in this case, 4:5. To solve this, we need to find out how many parts in total are there and then how many trophies each part represents.
We start by adding the parts of the given ratio: 4 + 5 = 9 parts. Since Brady has 36 trophies in total, we divide 36 by 9 to find out how many trophies represent one part: 36 ÷ 9 = 4 trophies per part. To get the number of trophies for each group, we multiply the number of trophies per part by the number of parts for each group. So for the first group (4 parts), we have 4 x 4 = 16 trophies and for the second group (5 parts), we have 5 x 4 = 20 trophies.
So the answer is a) 16 in the first group, 20 in the second group.