Ask yourself: does the number of months, $m$, affect the sign-up fee or the monthly fee? The number that repeats each month should be multiplied by $m$.

Since Emma is paying both the sign-up fee and the monthly fees, should those amounts be added together or should one be subtracted from the other?

Once you have an expression for Emma's total cost in terms of $m$, remember to set it equal to the total amount she paid, $205.

In Desmos, let $m$ be represented by $x$ (Desmos uses $x$ as the default variable), so think of each equation as involving $x$ instead of $m$.

Type the left side of each answer choice into its own line in Desmos, solving each for $y$. For example, for an option like $30m + 25 = 205$, rewrite it as $y = 30x + 25$ (ignore the $= 205$ for now) to represent the total cost after $x$ months.

For each expression you entered (such as $y = 30x + 25$ or $y = 25x + 30$), tap the table icon to create a table. Check what $y$ equals when $x = 0$ and when $x = 1$. The correct model will give the one-time fee when $x = 0$ and the sum of the sign-up fee plus one month of charges when $x = 1$; choose the option whose expression matches those values.

The problem describes two kinds of fees:

• A one-time sign-up fee of $25 (this is paid only once, not multiplied by months).
• A monthly fee of $30 (this is paid every month, so it repeats $m$ times).

For $m$ months:

• The total monthly cost is $30m$ because Emma pays $30 each month for $m$ months.
• The one-time sign-up fee is $25.

So, the total amount Emma pays after $m$ months is the sum of these: $30m + 25$.

The question says Emma paid a total of $205. That means the expression for her total cost must equal $205.

So we write the equation:

This matches choice C, so the correct answer is $30m + 25 = 205$.