**What is the least number of sunbirds that must pollinate the colony to ensure that it will survive until next year?**

To determine the least number of sunbirds that must pollinate the colony to ensure it will survive until next year, we start with the given inequality:

\[ 6H + 4S > 74 \]

We know from the problem statement that this year 8 hummingbirds (\(H = 8\)) pollinated the colony. Substituting \(H = 8\) into the inequality:

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

Calculate \(6 \times 8\):

\[ 48 + 4S > 74 \]

Next, subtract 48 from both sides to isolate the term with \(S\):

\[ 4S > 26 \]

Divide both sides by 4:

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

\[ S > 6.5 \]

Since the number of sunbirds (\(S\)) must be a whole number, we round up to the next integer greater than 6.5, which is 7.

Thus, the least number of sunbirds that must pollinate the colony to ensure its survival until next year is:

\[ \boxed{7} \]

Do you have any further questions or need more details?

Here are 5 additional questions you might find helpful:

1. How do you solve linear inequalities involving two variables?
2. What are common strategies for solving word problems involving inequalities?
3. Can you explain the significance of rounding up when dealing with inequalities in practical scenarios?
4. How would the result change if the inequality were different, say \(6H + 4S \geq 74\)?
5. What are some examples of inequalities in real-world situations? 

**Tip:** Always check your final answer by substituting it back into the original inequality to ensure it satisfies the condition given.

Discover how to determine the least number of sunbirds required for a colony's survival based on the inequality 6H + 4S > 74. The solution involves substituting values and solving for S, showing that at least 7 sunbirds are necessary. Ideal for Grades 7-9 students.

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