courses › Business Math

What a discount must earn back, who you can lose after a price rise, and bottleneck hours.

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

• Contribution after a discount par 14 s not tried yet

  worked example

  Price is $280 and variable cost is $125. A 5% price discount is offered. What is the new contribution per sale?

  Answer: $141.00

  1. New price = $280 × 0.95 = $266; contribution = $266 − $125 = $141, down from $155.
  2. The whole $14 discount comes out of contribution.

• Extra volume a discount needs par 24 s not tried yet

  worked example

  Price is $300 and variable cost is $240. After a 5% discount, by what percentage must sales volume rise to keep the same total contribution? Round to one decimal place if needed.

  Answer: 33.3%

  1. Contribution per sale falls from $300 − $240 = $60 to $285 − $240 = $45.
  2. Volume must rise by $60 ÷ $45 − 1 ≈ 33.3%.

• Price rise: customers you must keep par 21 s not tried yet

  worked example

  98 customers each contribute $470. A price increase would raise contribution to $560 per customer. What is the minimum whole number of customers needed to keep at least $46,060 of contribution?

  Answer: 83

  1. $46,060 ÷ $560 = 82.25; round up to 83.
  2. This is a threshold, not a forecast of how many will stay.

• Contribution per scarce hour par 17 s not tried yet

  worked example

  Job A contributes $620 in 4 scarce work hours. Job B contributes $1,400 in 7 scarce work hours. Which earns more contribution per scarce hour?

  1. Job B
  2. They are equal
  3. Job A
  4. You need the selling prices to decide

  Answer: Job B

  1. Per hour: A = $620 ÷ 4 = $155; B = $1,400 ÷ 7 = $200.
  2. When hours are the limit, rank jobs by contribution per scarce hour (assuming there's enough demand).

• Which price makes the most profit? par 45 s not tried yet

  worked example

  Price $85, variable cost $38 per unit, fixed costs $12,000 a month, 455 units a month now, capacity 590 units. Option 1: raise the price to $92 and sell 410 units. Option 2: cut the price to $80 and sell 554 units. Which gives the highest monthly operating profit?

  1. Option 1 (raise price)
  2. All three are equal
  3. Keep the current price
  4. Option 2 (cut price)

  Answer: Option 2 (cut price)

  1. Profit = units × (price − variable) − fixed: now $9,385, Option 1 $10,140, Option 2 $11,268.

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

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