Question

approaching notes/learning:
goal:
we will learn about how to calculate profit/loss
from revenue and costs.
negative answer means loss.
positive answer means profit.
vocabulary: break-even means equat
break-even equation model:
total revenue = total cost (rate * # item + fixed cost).
key words for total revenue variable - charge, pay, or sell rate *
item.
activity 1:
the school charges each student $20 to go. the trip still costs $168 for the bus plus $14 per student for tickets. i
the number of students.
write an equation where the total revenue is the same as the total cost.
solve for n (the break-even point).
check your work by substituting your answer back into the equation.

Explanation:

Step1: Write the equation

Let \(n\) be the number of students. Total Revenue \(= 20n\), Total Cost \(=14n + 168\). The break - even equation is \(20n=14n + 168\).

Step2: Solve the equation for \(n\)

Subtract \(14n\) from both sides:
\(20n-14n=14n + 168-14n\)
\(6n=168\)
Divide both sides by \(6\):
\(n=\frac{168}{6}\)
\(n = 28\)

Step3: Check the work

Substitute \(n = 28\) into the original equation.
Left - hand side (Total Revenue): \(20\times28=560\)
Right - hand side (Total Cost): \(14\times28+168=392 + 168=560\)

Answer:

The break - even equation is \(20n=14n + 168\) and the break - even point \(n = 28\)