Question 621·Medium·Algebra

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3x + 45 = 120

An online store charges a one-time membership fee of $45 plus $3 for each shipment. The equation above relates the total amount, in dollars, that a customer paid to the store to the number of shipments $x$ that the customer received in one year. How many shipments did the customer receive?

A linear equation can model a fixed charge plus a charge that repeats for every item. A one-time fee is added once; only the per-item price is multiplied by the number of items. If the equation is already given, use a Desmos regression to find the unknown, then check what that unknown counts before choosing an answer.

Hints

Hint 1
A fixed fee is charged once, no matter how many shipments arrive. The per-shipment charge repeats. Which part of the equation changes when the number of shipments changes?
Hint 2
A solution makes both sides of an equation equal. In Desmos, replace $x$ with $x_1$ and $=$ with $\sim$ to find it. Then check what $x$ counts in the question.

Step-by-step

Interpret the charges, then solve in Desmos
Step 1
Connect the equation to the charges
The store charges $3 for each of $x$ shipments, so $3x$ is the shipment charge. The $45 is a fixed fee, so the given equation adds it once: $3x+45=120$ . Only the per-shipment charge gets multiplied by $x$ .
Step 2
Find the number of shipments
Type $3x_1+45\sim120$ . Replacing $x$ with $x_1$ and $=$ with $\sim$ makes this a regression: Desmos finds the value that makes the two sides equal rather than graphing $x$ . Under PARAMETERS, it shows $x_1=25$ . Since $x$ counts shipments, the customer received $25$ shipments. Choice C.

Question 621·Medium·Algebra

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Step-by-step

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