Heather can complete two problems in ten minutes, and when she started she had three problems done. joel can complete three problems in fifteen minutes, and when he started he had two problems done. if you include the number of problems that were complete when they started, when will they have completed between 30 and 50 problems?

If Heather can do 2 in 10 minutes, then that means that she can do 12 in 1 hour. If Joel can do 3 in 15 minutes, then it means that he can do 12 in 1 hour. Add the number of problems they can do total and that will go between 30 and 50. It is just "less than", not "less than or equal to" because you want to know when the total number goes between the numbers.
Therefore, the correct answer must be 30 < 24x + 5 < 50.

D.