Final answer:
To determine how many tomato plants Ralph's garden had to begin with, we set up a proportion using the given ratio 5:6 and the information that half of Inessa's plants were moved to Ralph's garden, totaling 850 plants. Solving the proportion, we find that Ralph originally had 566 tomato plants.
Step-by-step explanation:
The question asks us to solve a problem involving ratios and proportions in the context of transferring tomato plants between gardens. Initially, the ratio of the number of tomato plants in Inessa's garden to the number in Ralph's garden was 5:6. After moving half of the tomato plants from Inessa's garden to Ralph's, Ralph's garden had 850 tomato plants. We need to find how many tomato plants Ralph had at the beginning.
We can let x represent the original number of tomato plants in Ralph's garden. Since the ratio of Inessa to Ralph was 5:6, for every 5 plants in Inessa's garden, there were 6 in Ralph's. This means that half of Inessa's plants would be (5/6)x/2. After transferring, Ralph had x + (5/6)x/2 = 850 plants. Simplifying, we get (3/2)x = 850. Solving for x gives x = 850 × (2/3) = 566.67. Since we can't have a fraction of a plant, we round down to the nearest whole number, which is 566 plants. Ralph had 566 tomato plants to begin with.