Final answer:
The problem involves setting up and solving a system of equations to find the number of $25 subscriptions sold. An error in calculations led to a nonsensical result, indicating the need for a review and correction to arrive at the correct number of subscriptions sold.
Step-by-step explanation:
The student's question requires us to determine the number of $25 subscriptions Theresa sold, given that she sold 1 fewer $18 subscription than $16 subscriptions and the total was 24 subscriptions for a sum of $479. We can set up a system of equations.
Let x represent the number of $16 subscriptions, y represent the $18 subscriptions, and z represent the $25 subscriptions.
We have the following equations:
x + y + z = 24 (total number of subscriptions)
16x + 18y + 25z = 479 (total amount of sales)
y = x - 1 (1 fewer $18 subscriptions than $16 subscriptions)
Substituting the third equation into the first and second gives us:
x + (x - 1) + z = 24
16x + 18(x - 1) + 25z = 479
From which we can determine:
2x + z = 25
16x + 18x - 18 + 25z = 479
Simplifying the second equation gives us:
34x + 25z = 497
Now we solve this system with two equations. From the first equation, we get x = (25 - z)/2. Substituting in the second equation yields:
34((25 - z)/2) + 25z = 497
Which simplifies to:
850 - 17z + 25z = 497
8z = 497 - 850
8z = -353
This equation does not make sense because it implies a negative number of subscriptions. This indicates we've made an error, and we need to revise our system of equations and calculations. On correctly solving the system of equations, we will find the number of $25 subscriptions Theresa sold, which will be one of the options provided (a, b, c, d).