Final answer:
By setting up an equation based on the given ratios and the fact that half of Inessa's plants were moved to Ralph's garden, it can be determined that Ralph's garden had originally 600 tomato plants.
Step-by-step explanation:
The question is about calculating the original number of tomato plants in Ralph's garden based on given ratios and the effect of replanting half of the plants from Inessa's garden to Ralph's garden. We know the ratio of the number of tomato plants in Inessa's garden to Ralph's garden was 5:6, and after replanting, Ralph had 850 tomato plants.
To solve this, first denote the number of tomato plants in Inessa's garden as 5x and in Ralph's garden as 6x, where x is the common ratio factor. Then, when half of Inessa's plants are replanted in Ralph's garden, Ralph has the following number of plants:
6x + ½ × 5x = 850
Combining like terms, we get:
6x + 2.5x = 850
8.5x = 850
Divide both sides by 8.5 to find x:
x = 850 ÷ 8.5
x = 100
Now we can calculate the original number of plants in Ralph's garden by multiplying the common ratio factor by 6:
Ralph's original number of plants = 6 × 100
= 600
So Ralph's garden had 600 tomato plants to begin with, before any were replanted from Inessa's garden.