HSA.CED.A.1 Tutor Intake — Creating Equations and Inequalities

A student is solving a word problem and writes the following as their
first step:

"Let $x$ be the amount."

Which concern is most important to raise about this variable definition?

A gym charges a $40 enrollment fee and $25 per month. Maria's budget is
$215. Which of the following is the correct algebraic equation to find
how many months she can afford?

After solving an equation in a word problem, a student gets $x = -6$.
The problem asks for the number of boxes shipped. Which is the correct
next step?

A car rental company charges $30 per day plus $0.15 per mile. A
customer rented the car for 1 day and paid $97.50 total.

Let $m$ = miles driven. Write and solve the equation $30 + 0.15m = 97.50$.

How many miles did the customer drive?

A store needs to sell units at $12 each to cover $450 in fixed costs
and make a profit. Which inequality correctly models the number of units
$u$ the store must sell?

A rectangular garden has a perimeter of 32 meters. One side has length
$x$ meters, so the adjacent side has length $(16 - x)$ meters.

Set up and expand the area equation: $A = x(16 - x)$.

If the area equals 48 square meters, write the equation in standard form
$ax^2 + bx + c = 0$ and find the positive value of the constant $c$.