Question

1. complete the story so that it can be modeled by the inequality $9f + 28 \geq 100$.
2. fred is making spirit flags for his schools championship football game. fred wants to figure out how many flags, $f$, he needs to make per day in order to have at least ____ flags. he has already made __ flags, and there are ____ more days before the game.
3. select the true statement.
4. fred needs to make at least 8 flags per day.

fred needs to make at most 8 flags per day.
fred needs to make at least 9 flags per day.
fred needs to make at most 9 flags per day.

Explanation:

Step1: Match inequality to story

The inequality is $9f + 28 \geq 100$. Here, $9$ = number of days left, $28$ = flags already made, $100$ = total minimum flags needed.

Step2: Solve for daily flags $f$

Subtract 28 from both sides:
$9f + 28 - 28 \geq 100 - 28$
$9f \geq 72$
Divide both sides by 9:
$\frac{9f}{9} \geq \frac{72}{9}$
$f \geq 8$

Step3: Fill story blanks

From the inequality, total minimum flags = 100, flags made = 28, days left = 9.

Step4: Identify true statement

$f \geq 8$ means at least 8 flags per day.

Answer:

Completed Story:

Fred is making spirit flags for his school's championship football game. Fred wants to figure out how many flags, $f$, he needs to make per day in order to have at least $\boldsymbol{100}$ flags. He has already made $\boldsymbol{28}$ flags, and there are $\boldsymbol{9}$ more days before the game.

True Statement:

Fred needs to make at least 8 flags per day.