A set of scales is used to show that two lemons and seven tomatoes are required to balance one cabbage. If two lemons balance one tomato, how many tomatoes will balance one cabbage?

2 lemons + 7 tomatoes = 1 cabbage
Since 2 lemons = 1 tomato,
(1 tomato) + 7 tomatoes = 1 cabbage
8 tomatoes = 1 cabbage
Therefore, the number of tomatoes that will balance 1 cabbage is 8.

Let's solve this algebraically:
let: tomatoes be y
lemons be x

Our equation for the first statement would be: 2x + 7y = 1 ___ (1)
Given that 2 lemons equals 1 tomato, 2x = y, x = y/2 ___ (2)

By subbing equation (2) into equation (1), we can attain the number of tomatoes that balances 1 cabbage. So, 2(y/2) + 7y = 1
8y = 1
This means that we need 8 tomatoes to balance 1 cabbage. Thus, the answer is 8 tomatoes.