Question 13·Easy·Linear Equations in One Variable

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During a promotional period, an online movie service charged a flat subscription fee of $12 for the month plus $7 for each movie rented. If Nadine’s total charge for the month was $89, how many movies did she rent that month?

A linear equation models a flat charge plus the same added charge for each item. Let $x$ count the items, multiply only the per-item price by $x$ , and set the total equal to the bill. In Desmos, a regression finds the count that makes the equation true. The trap is multiplying the flat fee by $x$ too, even though it’s paid only once.

Hints

Hint 1
A flat fee is paid once, no matter how many movies Nadine rents. If $x$ counts movies, which charge grows with $x$ , and which charge stays the same?
Hint 2
A rate of $7 per movie makes the rental charge $7x$ dollars for $x$ movies. Add the fee to get the total charge. What equation matches that total to Nadine’s bill?

Step-by-step

Model the bill and solve in Desmos
Step 1
Write an equation for the total charge
Let $x$ be the number of movies Nadine rented. At $7 per movie, the rentals cost $7x$ dollars. The $12 subscription fee is flat: she pays it once, not for every movie. Multiply the per-movie charge by $x$ , but add the flat fee only once. Those charges make up the $89 bill, so
$12+7x=89.$
Step 2
Find the number of movies
Type $12+7x_{1}\sim89$ in Desmos. Use $x_1$ instead of $x$ so Desmos solves for the count rather than graphing it; $\sim$ asks Desmos to match the two sides. Under PARAMETERS, it shows $x_1=11$ . Since the unknown counts movies, Nadine rented 11 movies. Choice C.

Question 13·Easy·Linear Equations in One Variable

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Strategy

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