Courses · Business Mathematics · Week 8

Weighted Averages & Product Mix

Week 8 of Business Mathematics, a fifteen-week course taught through Food Truck Wars, a live business simulation. Free to read; the practice boxes check your arithmetic as you go.

Nobody lines up for a truck's fries. But the fries and drinks riding along add more than half again to what each burger buyer is worth. This week you count the whole order.

Learning objectives. After this week you can (1) compute a weighted average and say why it beats a simple average; (2) measure your attach rates from your own Daily Report; and (3) compute your blended contribution margin and what one hero customer is worth.

Remember this: a customer is worth the whole order, not just the burger.

1) The weighted average

Weighted Average = Σ(value × units) ÷ Σ(units)

A simple average counts every item once. A weighted average counts each item as often as you sell it. Sell 150 burgers at $8.00 and 50 fries at $4.00, and the average price is not $6.00. It is (150 × 8 + 50 × 4) ÷ 200 = 1,400 ÷ 200 = $7.00, because burgers carry three times the weight. Sell more of your lowest-margin item and the average margin falls, even if total units look great.

2) Attach rates: the shape of your mix

Attach Rate = Attached Units ÷ Hero Units

Your hero is the item people come for. In Food Truck Wars, sides and drinks never sell on their own: they attach to hero sales. Sell 200 burgers with 110 fries and 150 drinks, and the side attach rate is 110 ÷ 200 = 0.55; the drink rate is 150 ÷ 200 = 0.75. Always divide by the hero count, using the units sold on your own report.

Try it

You sold 296 burgers and 144 portions of fries beside them.

Attach rate % = Side units ÷ Hero units × 100

Fill in the boxes.

3) Blended contribution margin

Blended CM per item = Total Contribution ÷ Total Items
Contribution per hero customer = Total Contribution ÷ Hero Units

Same day: burgers $8.50 (cost $3.20, CM $5.30), fries $4.50 (cost $1.60, CM $2.90), drinks $2.80 (cost $1.10, CM $1.70).

  • Total contribution = 200 × 5.30 + 110 × 2.90 + 150 × 1.70 = 1,060 + 319 + 255 = $1,634.
  • Blended CM = 1,634 ÷ 460 items ≈ $3.55. The simple average of the three CMs, $3.30, is wrong: it ignores how many of each you sold.
  • Per hero customer = 1,634 ÷ 200 = $8.17, not the burger's $5.30.

Blended CM is also the one to use for a break-even in items when you sell a mix: fixed costs ÷ blended CM. Swap CM for prices and the same idea gives the revenue one customer brings: hero price + side price × side attach rate + drink price × drink attach rate.

Try it

A $12.50 burger, $6.50 fries, and 49% of burger buyers take the fries.

Basket = Hero price + (Side price × Attach rate)

Fill in the boxes.

Quick self-check

You sell 120 burgers (CM $5.30), 60 fries (CM $2.90) and 96 drinks (CM $1.70). (a) Attach rates? (b) Total contribution? (c) Contribution per hero customer? (Answers: 60 ÷ 120 = 0.50 and 96 ÷ 120 = 0.80; 636 + 174 + 163.20 = $973.20; 973.20 ÷ 120 = $8.11.)

Common mistakes

  • Simple-averaging when quantities differ. Weight every average by units sold.
  • Dividing by total units. An attach rate divides by hero units only.
  • Valuing a customer at the hero's CM. Count the fries and drink that came along.

This week in the arena

Pull one Daily Report. From its units sold, compute your side and drink attach rates, then use the prices and unit costs on your decision form to find what one hero customer contributed. Is a burger buyer worth more or less to your truck than your crew guessed? Bring that number to your team discussion.

In the course, the reading is where the week starts

Students who take Business Mathematics on Extrapoli run a business in Food Truck Wars all term. Each week pairs this reading with a quiz and a two-part assignment worked from the numbers their own team produced in the simulation, and the numbers are graded automatically against the simulation that team actually ran.