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To solve this problem, we need to determine the least number of sunbirds (S) required for the colony to survive, given that \( H = 8 \).

The inequality provided is:

\[ 6H + 4S > 74 \]

Substitute \( H = 8 \) into the inequality:

\[ 6(8) + 4S > 74 \]

Simplify the expression:

\[ 48 + 4S > 74 \]

Subtract 48 from both sides:

\[ 4S > 26 \]

Divide both sides by 4:

\[ S > \frac{26}{4} \]

\[ S > 6.5 \]

Since \( S \) must be an integer, the smallest integer greater than 6.5 is 7.

Therefore, the least number of sunbirds that must pollinate the colony to ensure it will survive until next year is 7.

The correct answer is:

\[ \boxed{\text{C. At least 7 sunbirds must pollinate the colony.}} \]

Do you have any questions or need further details? 

Here are 5 more questions you might want to ask:

1. How do you solve linear inequalities with one variable?
2. What are some real-life applications of solving inequalities?
3. Can you explain the concept of integer constraints in inequalities?
4. How would the solution change if the number of hummingbirds varied?
5. What methods can be used to graph the inequality \( 6H + 4S > 74 \)?

**Tip:** When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the problem of determining the least number of sunbirds required for a colony's survival with a step-by-step solution. This problem involves solving linear inequalities and integer constraints. Suitable for students in Grades 7-9.

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