Question 125·Medium·Linear Equations in One Variable
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 that the customer received in one year. How many shipments did the customer receive?
For linear equations that model a total cost with a fixed fee plus a per-item charge, treat it like any one-variable equation: first undo the addition or subtraction to isolate the term with the variable, then undo the multiplication or division to solve for the variable. Doing the inverse operations in this order, and quickly checking by substituting your answer back into the original equation, helps avoid simple arithmetic mistakes on the SAT.
Hints
Focus on the fixed fee vs. shipment cost
In the equation , which part is the one-time membership fee and which part depends on the number of shipments?
Isolate the variable term first
Think about how to remove the from the left side so that only the term is left. What operation undoes adding ?
Solve once is alone
After you find by itself on one side of the equation, what should you do to get by itself?
Desmos Guide
Use Desmos to compute the value of x
In a Desmos expression line, type (120 - 45) / 3 and press Enter. The value that Desmos outputs is the number of shipments the customer received.
Step-by-step Explanation
Understand the equation
The equation
represents:
- : total cost for shipments at $3 each
- $45: one-time membership fee
- $120: total amount paid
We need to solve this equation for , the number of shipments.
Isolate the shipment term
To get the term alone, subtract from both sides of the equation:
Now we know the total cost of the shipments alone is $75.
Solve for the number of shipments
Now divide both sides by to solve for :
So, the customer received 25 shipments, which corresponds to choice C.