Final answer:
There are 56 cabbage plants in Mr. Green's garden, determined by solving proportion and subtraction based on the ratio of tomato to cabbage plants and the total count of plants.
Step-by-step explanation:
To determine how many cabbage plants are in Mr. Green's garden, we can use a ratio based on the information that for every 6 tomato plants there are 14 cabbage plants, resulting in a total of 80 tomato and cabbage plants combined. Let's define T as the number of tomato plants and C as the number of cabbage plants.
Given the ratio 6:14 (tomatoes:cabbages), we can write it as 6/20 = T/(T+C) where T+C = 80 because the total number of plants is 80. Multiplying both sides of the equal sign by 20(T+C) gives us 6(T+C) = 20T. Substituting 80 for T+C gives us 6(80) = 20T or 480 = 20T. Solving for T gives T = 480/20 = 24. Therefore, there are 24 tomato plants in the garden.
To find the number of cabbage plants, subtract the number of tomato plants from the total number of plants: C = 80 - T, which is C = 80 - 24 = 56. Thus, there are 56 cabbage plants in Mr. Green's garden.