doing math

courses › Business Math

Solve for the Unknown

level 8 course

Turn a business target into a simple equation and solve it.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 8.

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Builds on: First Business Story

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Turn the story into an equation with a named unknown. Revenue = price × count means a count is revenue ÷ price. For a profit target, each customer's contribution (what each one leaves after its own variable costs) has to pay the fixed costs and the target.

Many costs are a fixed amount plus a cost per job. With $2,000 fixed and $50 a job, 100 jobs cost $7,000 in all, an average of $70 a job. But one more job adds only $50, because the $2,000 is paid either way.

Techniques

Write it, then undo it

A count for a revenue or profit target.

  1. Write it out: price × count = revenue, or contribution × customers = fixed costs + target.
  2. Divide both sides by the amount per customer or per unit.
  3. People and jobs come in whole numbers: round up, then check.
worked example

Example: Each customer leaves $300 a month after variable costs. Fixed monthly costs are $4,500. How many whole customers are needed for at least $2,000 of monthly operating profit?

  1. $300 × customers must cover $4,500 + $2,000 = $6,500.
  2. $6,500 ÷ $300 ≈ 21.67, so round up to 22.
  3. Check: 21 customers bring $6,300, short of $6,500.

Answer: 22

Extra cost: the per-job part

Total cost is a fixed amount plus a cost per job, and the number of jobs changes.

  1. Count the extra jobs: new number minus old.
  2. Multiply by the cost per job.
  3. Leave the fixed amount out. It is paid either way.
worked example

Example: Total cost is $1,500 plus $25 per job. How much does total cost rise when jobs go from 80 to 100?

  1. 100 − 80 = 20 extra jobs.
  2. 20 × $25 = $500.

Answer: $500

Average cost: total ÷ jobs

The average cost per job at a given number of jobs.

  1. Total cost: the fixed amount plus the cost per job × the jobs.
  2. Divide the total by the number of jobs.
worked example

Example: Total cost is $3,000 plus $40 per job. What is the average cost per job at 150 jobs?

  1. Total: $3,000 + $40 × 150 = $9,000.
  2. Average: $9,000 ÷ 150 = $60.

Answer: $60

Tips by skill

  • TipHow many to hit a revenue target?: Revenue = price × count, so divide the revenue by the price. Multiply back to check.
  • TipCustomers for a profit target: Add the fixed costs and the profit target, divide by what each customer leaves, and round up.
  • TipHow much does cost rise?: Only the per-job part grows. Multiply the extra jobs by the cost per job; the fixed amount is paid either way.
  • TipAverage cost per job: Find the total cost first: the fixed amount plus the cost per job × the jobs. Then divide by the jobs.

Watch out for

  • Covering the fixed costs but forgetting the profit target. The customers have to pay for both.
  • Rounding part of a customer down. 21.67 customers means 22, because 21 falls short.
  • Using the average cost for each extra job. At 150 jobs the average is $60, but one more job adds only $40.
  • Answering in dollars when the question asks for a count.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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