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To find the number of roses and tulips in the garden, we can set up two equations using the given information and solve them simultaneously.
Let's assume the total number of roses in the garden is represented by R, and the total number of tulips is represented by T. From the given information, we know that 40% of the roses are in bloom, which means 0.4R roses are in bloom. Similarly, 20% of the tulips are in bloom, which means 0.2T tulips are in bloom. According to the question, the number of roses and the number of tulips yet to bloom are the same. So, the number of roses yet to bloom is 0.6R, and the number of tulips yet to bloom is 0.8T.
Since the total number of flowers in bloom is 1100, we can write the equation: 0.4R + 0.2T = 1100. Similarly, since the number of roses yet to bloom is the same as the number of tulips yet to bloom, we can write the equation: 0.6R = 0.8T.
We can solve these two equations simultaneously to find the values of R and T.