GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A small business sells custom-made phone cases. The cost (C) to produce 'x' cases is given by C(x) = 15x + 300, and the revenue (R) from selling 'x' cases is given by R(x) = 35x. How many cases must the business sell to break even?
- A25 cases
- B10 cases
- C15 cases
- D20 cases
Show answer & explanationAnswer & explanation
Correct answer: C. 15 cases
To break even, the cost must equal the revenue. By setting the cost function equal to the revenue function, we can solve for the number of cases 'x'.
Why the other options are wrong
- A. At 25 cases: C(25) = 15(25) + 300 = 375 + 300 = 675; R(25) = 35(25) = 875. Profit, not break even.
- B. At 10 cases: C(10) = 15(10) + 300 = 450; R(10) = 35(10) = 350. Not break even.
- D. At 20 cases: C(20) = 15(20) + 300 = 600; R(20) = 35(20) = 700. Profit, not break even.
Break-Even Point (Linear Functions)
The point at which total cost equals total revenue, resulting in zero profit or loss. For linear cost and revenue functions, it's found by setting C(x) = R(x) and solving for x.
- Cost function (C(x)) typically includes fixed and variable costs.
- Revenue function (R(x)) is price per unit times quantity.
- Solving C(x) = R(x) gives the quantity needed to break even.
Memory trick: Costs Catch Revenue, Zero Results.