Question 130·Easy·Linear Equations in One Variable
A gym charges a one-time registration fee and then $25 per month for membership. Julio paid a total of $175 for 5 months of membership. What is the one-time registration fee, in dollars? Aniкo Questіоn Banк
(Express the answer as an integer)
For this kind of SAT word problem, first translate the situation into a simple equation: total cost = one-time fee + (monthly cost × number of months). Plug in the numbers from the problem, simplify the multiplication, and then isolate the unknown (the fee) using one inverse operation, usually subtraction. Writing a short equation instead of trying to reason it out in words helps avoid mixing up which amount is monthly and which is one-time, and makes your calculations faster and more reliable. A-n-i-к-ο.аi
Hints
Identify the two parts of the total cost
Julio’s total payment is made of two pieces: a one-time registration fee and the monthly charges. Which of these depends on the number of months, and which does not?
Find the total monthly charges
If Julio pays dollars each month for 5 months, how much money in total goes toward the monthly membership charges?
Relate total paid to the registration fee
Once you know how much he paid just for the 5 months, subtract that amount from . What does the leftover amount represent? A-n-i-к-о.аi
Desmos Guide
Use Desmos to compute the registration fee
In Desmos, type the expression 175 - 25*5 and look at the numeric result. That value is the one-time registration fee in dollars.
Step-by-step Explanation
Define the unknown and set up the equation
Let be the one-time registration fee (in dollars).
Julio paid for 5 months at per month, so the total monthly charges are dollars per month times months.
The total he paid is the registration fee plus the monthly charges:
Calculate the total monthly cost for 5 months
Compute the cost of 5 months at per month:
So the equation becomes:
Isolate the registration fee
To solve for , subtract from both sides of the equation:
which simplifies to:
Compute the difference and state the answer
Now calculate :
So the one-time registration fee is $50.