A colony of flowers is pollinated by hummingbirds and sunbirds. $\newline$ Let $\newline$ $H$ represent the number of hummingbirds and $\newline$ $S$ represent the number of sunbirds that must pollinate the colony so it can survive until next year. $\newline$ $6H+4S > 74$ $\newline$ This year, $8$ hummingbirds pollinated the colony. What is the least number of sunbirds that must pollinate the colony to ensure that it will survive until next year? $\newline$ Choose $1$ answer: $\newline$ (A) At least $4$ sunbirds must pollinate the colony. $\newline$ (B) At least $6$ sunbirds must pollinate the colony. $\newline$ (C) At least $7$ sunbirds must pollinate the colony. $\newline$ (D) At least $8$ sunbirds must pollinate the colony.

View step-by-step help

Home

Math Problems

Algebra 1

Modeling with linear inequalities

Full solution

Q. A colony of flowers is pollinated by hummingbirds and sunbirds.

\newline

Let

\newline

H

represent the number of hummingbirds and

\newline

S

represent the number of sunbirds that must pollinate the colony so it can survive until next year.

\newline

6H+4S > 74

\newline

This year,

8

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

\newline

Choose

1

answer:

\newline

(A) At least

4

sunbirds must pollinate the colony.

\newline

(B) At least

6

sunbirds must pollinate the colony.

\newline

7

sunbirds must pollinate the colony.

\newline

(D) At least

8

sunbirds must pollinate the colony.

Understand the inequality: Understand the inequality that represents the condition for the colony's survival. $\newline$ The inequality given is $6H + 4S > 74$ , where $H$ is the number of hummingbirds and $S$ is the number of sunbirds. We need to find the minimum value of $S$ when $H$ is given as $8$ .
Substitute $H$ into the inequality: Substitute the value of $H$ into the inequality. $\newline$ Since we know that $8$ hummingbirds have pollinated the colony, we substitute $H = 8$ into the inequality to find the minimum number of sunbirds needed. $\newline$ $6(8) + 4S > 74$
Perform multiplication to simplify: Perform the multiplication to simplify the inequality. $\newline$ $6(8)$ gives us $48$ , so the inequality becomes: $\newline$ $48 + 4S > 74$
Isolate the variable $S$ : Isolate the variable $S$ by subtracting $48$ from both sides of the inequality. $\newline$ $4S > 74 - 48$ $\newline$ $4S > 26$
Divide both sides of the inequality: Divide both sides of the inequality by $4$ to solve for $S$ . $\newline$ $S > \frac{26}{4}$ $\newline$ $S > 6.5$
Determine the minimum number of sunbirds: Since $S$ must be an integer (you can't have half a sunbird), and the inequality is strict ( $S > 6.5$ ), the least number of sunbirds that must pollinate the colony is $7$ .
Choose the correct answer: Choose the correct answer from the given options. $\newline$ The correct answer is (C) At least $7$ sunbirds must pollinate the colony.