Set up $A(w)<B(w)$ and solve for $w$. A-n-i-k-o.аі

After solving the inequality, convert the result into the correct statement about positive integer values of $w$.

In Desmos, type w=1 to create a slider, then restrict yourself to positive integers for testing.

Enter

• A = 360 + 12*(110 + 70*(w-1))
• B = 200 + 12*(80*w) Ani​k⁠о - Freе Ѕ‍АТ Рreр

Compute A-B (or graph both and look for when $A$ is below $B$). The switch happens just after $w=5$, so for positive integers Plan A is cheaper for $w\ge 6$.

For $w$ weeks, each student pays $110 for the first week and $70 for each of the remaining $w-1$ weeks.

So Plan A’s total cost is

Plan B charges $80 per student per week plus a $200 facility fee, so

First simplify each expression:

and

Now solve:

Since $w$ must be a positive integer and $w>\frac{16}{3}\approx 5.33$, the solutions are

So the correct choice is $w\ge 6$. © an​ikο.а‍і